Dataset Viewer
id
string | setting_key
string | messages
list | ground_truth
string | dataset
string |
|---|---|---|---|---|
algebra_func_area_train_0000 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2|(1(-2cos(1π(3x - 2) - 1) - 1)^2 + 3(-2cos(1π(3x - 2) - 1) - 1) - 1) + 2| - 1 and g(x) = -3cos(2π((-1(-3|x - 1| + 3))/(-2(-3|x - 1| + 3) - 1))) - 2 from x = 2.1 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0001 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4(5(2|x - 3| - 1)^2 + 4(2|x - 3| - 1) - 2) + 5 and g(x) = (3(2x^2 + 4x + 3) + 1)/(1(2x^2 + 4x + 3)) from x = 2.3 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 13.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0002 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3x^2 - 4x + 2) - 2)/(-2(-3x^2 - 4x + 2) - 2) and g(x) = -5x^2 + 3x - 2 between the vertical lines x = -1.9 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 24.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0003 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3((2x - 1)/(-2x + 3))^2 - 2((2x - 1)/(-2x + 3)) - 2, g(x) = (-1x + 1)/(-3x + 2), x = -1.1, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 7.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0004 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3|((1(-3sin(2πx + 1) - 2) - 3)/(1(-3sin(2πx + 1) - 2)))| - 2 and g(x) = 1|(-3x^2 + 4x - 1) - 3| - 1 from x = 3.7 to x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 8.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0005 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3|(1x^2 + 2x - 2)| + 1 and g(x) = 3|x + 3| - 1 from x = -2.9 to x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0006 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-1(3(1e^(-1(-3|x + 1| + 3)) - 2)^2 + 3(1e^(-1(-3|x + 1| + 3)) - 2) - 2) - 2)/(3(3(1e^(-1(-3|x + 1| + 3)) - 2)^2 + 3(1e^(-1(-3|x + 1| + 3)) - 2) - 2) + 1), g(x) = -3sin(3π((-1(-2|x - 1| - 3))/(-2(-2|x - 1| - 3) - 3)) - 3) + 2, x = -4.8, and x = -2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0007 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 5((1(2|x - 2| - 3) - 3)/(3(2|x - 2| - 3)))^2 + 1 and g(x) = -2sin(3π(3x + 2) + 1) + 2 from x = -3.3 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0008 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 5(2sin(1π((2x + 3)/(-3x)) - 2) - 2) - 5 and g(x) = (2(3cos(3πx - 3) - 2) - 2)/(2(3cos(3πx - 3) - 2) + 3) from x = 4.2 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0009 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (3(-1(3|(3x + 5) + 2| - 1)^2 + 3(3|(3x + 5) + 2| - 1)) - 1)/(1(-1(3|(3x + 5) + 2| - 1)^2 + 3(3|(3x + 5) + 2| - 1)) + 3), g(x) = 2(-3e^(-1(-1|x| + 3)) - 2)^2 + 4(-3e^(-1(-1|x| + 3)) - 2) - 2, x = -2.9, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 33.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0010 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((-3x - 3)/(2x)) - 1| + 2 and g(x) = -4x^2 - 2x + 3 between the vertical lines x = -0.7 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0011 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-3(5(-5(3|x + 2| + 1) - 4)^2 - 1(-5(3|x + 2| + 1) - 4) + 3) - 3)/(2(5(-5(3|x + 2| + 1) - 4)^2 - 1(-5(3|x + 2| + 1) - 4) + 3) - 1), g(x) = -5(-3sin(2π(2|x - 1| - 3) + 1) + 2)^2 + 4(-3sin(2π(2|x - 1| - 3) + 1) + 2) - 1, x = 3.1, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0012 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4(5((-2x + 2)/(1x)) - 1)^2 + 2(5((-2x + 2)/(1x)) - 1) + 2 and g(x) = -1(3|x + 1|)^2 + 1(3|x + 1|) - 1 from x = 0.7 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 10.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0013 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(3sin(1πx + 1) + 3)| + 2 and g(x) = (-3x + 3)/(-1x - 2) between the vertical lines x = -4.5 and x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 9.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0014 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(2x^2 - 1x - 3) + 1 and g(x) = 1x - 1 between the vertical lines x = -1.2 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 25.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0015 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(1π(2|x + 1|) - 1) and g(x) = (-2x)/(2x) between the vertical lines x = 1.9 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0016 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-2|((-1x + 1)/(3x)) + 3| - 2) - 2 and g(x) = -1((3x - 2)/(-3x - 1))^2 + 2((3x - 2)/(-3x - 1)) + 2 between the vertical lines x = -0.6 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| -19.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0017 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(4(-1(-2|x - 3| + 2) - 2)^2 - 4) - 2)/(-1(4(-1(-2|x - 3| + 2) - 2)^2 - 4)) and g(x) = (3(-5(3x + 4)^2 + 1) + 1)/(-2(-5(3x + 4)^2 + 1) + 1) from x = -1.2 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 11.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0018 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1|(-1(2e^(-2x) + 1)^2 - 3(2e^(-2x) + 1) + 2)| - 3, g(x) = -2(3sin(2πx + 2) + 1)^2 - 3(3sin(2πx + 2) + 1) + 5, x = 0.3, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0019 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-3cos(1πx - 1) + 2) + 2)/(2(-3cos(1πx - 1) + 2)) and g(x) = -2x + 4 between the vertical lines x = 2.0 and x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 6.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0020 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((2(-2e^(-2x) + 3) + 1)/(2(-2e^(-2x) + 3)))^2 - 3((2(-2e^(-2x) + 3) + 1)/(2(-2e^(-2x) + 3))) - 2 and g(x) = -3cos(3π(-2x^2 - 1x + 3) - 3) between the vertical lines x = 3.8 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0021 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(-3cos(3π(2x^2 + 4x - 3) - 2) + 1) - 3)/(1(-3cos(3π(2x^2 + 4x - 3) - 2) + 1)) and g(x) = (-1(-5x + 2) + 3)/(-2(-5x + 2) - 3) from x = 2.8 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0022 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-2(-1(3cos(1πx + 1))^2 - 5(3cos(1πx + 1)) - 5) - 2)/(-3(-1(3cos(1πx + 1))^2 - 5(3cos(1πx + 1)) - 5) - 2), g(x) = 3|(2x - 5) - 2|, x = 3.6, and x = 4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0023 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((3(-3|(-1sin(3πx + 1) + 1) - 1| + 2) + 1)/(1(-3|(-1sin(3πx + 1) + 1) - 1| + 2) + 3)) and g(x) = 3cos(3π(-4(5x + 3)^2 - 3(5x + 3) + 3) - 3) between the vertical lines x = 1.8 and x = 1.9000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0024 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1|x - 3| - 3)^2 - 4(-1|x - 3| - 3) + 5 and g(x) = -3x + 4 between the vertical lines x = 2.7 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0025 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(-3|(-3cos(3πx - 2) - 1) + 1| + 1) + 3)/(1(-3|(-3cos(3πx - 2) - 1) + 1| + 1) + 3) and g(x) = -3cos(3π(-1x^2 + 5x - 5) - 3) + 3 from x = -3.9 to x = -3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0026 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(1|(-1((3x)/(3x - 2))^2 - 3((3x)/(3x - 2)) + 4) + 1| - 3) + 2 and g(x) = (-2(1(-3e^(1x) - 1)^2 - 2(-3e^(1x) - 1) - 4) - 1)/(1(1(-3e^(1x) - 1)^2 - 2(-3e^(1x) - 1) - 4) - 2) between the vertical lines x = 0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0027 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1(3sin(3πx - 1) - 3) - 2 and g(x) = 3x - 3 from x = -1.5 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0028 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (2(1|(1x - 3) + 3| + 1) - 3)/(3(1|(1x - 3) + 3| + 1) + 3), g(x) = (2(-2x^2 + 1x + 4) - 3)/(1(-2x^2 + 1x + 4)), x = -0.9, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0029 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1e^(-2(-1(2|x + 1| - 3)^2 + 1(2|x + 1| - 3) + 3)) - 1 and g(x) = -2sin(1π(1x - 4)) from x = -0.2 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0030 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2π(3x + 3) + 1) - 3 and g(x) = (-1x + 1)/(1x + 3) between the vertical lines x = -4.6 and x = -4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0031 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (1(-1x^2 + 3x - 4) - 1)/(3(-1x^2 + 3x - 4) + 3), g(x) = (-1x - 2)/(-2x - 1), x = 1.0, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0032 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3|(-4x + 2)| + 1 and g(x) = (-2x + 1)/(-1x + 2) from x = 0.6 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 5.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0033 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 4(-3|(-1cos(3πx + 1) + 1)| + 3)^2 - 1(-3|(-1cos(3πx + 1) + 1)| + 3) - 2 and g(x) = (-1(1x^2 + 5x + 1) - 2)/(3(1x^2 + 5x + 1) + 2) from x = 0.1 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 6.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0034 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((2(1|x + 2| - 1) - 2)/(2(1|x + 2| - 1) - 1)) and g(x) = -5(-1e^(-1x) + 3) - 5 between the vertical lines x = -1.0 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0035 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(1|(-1x - 3) + 2| - 1)^2 + 2(1|(-1x - 3) + 2| - 1) - 3 and g(x) = -5(2|x| - 2)^2 - 5(2|x| - 2) from x = 0.3 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0036 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2|((1(2(4x^2 - 3x) - 2) - 3)/(-1(2(4x^2 - 3x) - 2) + 2)) + 2| + 1 and g(x) = -5(3|((-3x + 1)/(3x + 3)) - 2| - 2) + 4 from x = -0.6 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0037 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π(2x - 5) + 1) - 1 and g(x) = (-2x - 1)/(2x - 3) between the vertical lines x = -1.7 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0038 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1((3(-2x^2 - 3x + 3) - 3)/(-2(-2x^2 - 3x + 3) - 1)) + 5, g(x) = 2(-2sin(1πx - 3) - 1)^2 - 3, x = 1.8, and x = 3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 6.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0039 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4(-2e^(1x) + 2)^2 - 3(-2e^(1x) + 2) + 2 and g(x) = 3x^2 - 3x - 4 from x = -0.4 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 4.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0040 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-2|x + 2| - 2) - 1)/(2(-2|x + 2| - 2)) and g(x) = 2x^2 - 2x - 5 between the vertical lines x = -1.4 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 17.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0041 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1((3x - 3)/(2x + 1))^2 + 5((3x - 3)/(2x + 1)) - 4, g(x) = 3x^2 + 1x + 5, x = -2.2, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 4.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0042 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -5(3cos(2π((-2x + 2)/(1x)) - 2) + 3) + 1, g(x) = (-2(-3sin(2πx + 1) - 2) - 2)/(2(-3sin(2πx + 1) - 2) + 2), x = -0.2, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0043 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (1(1|(-5(1x + 3)^2 - 4(1x + 3) + 5)| - 1))/(-3(1|(-5(1x + 3)^2 - 4(1x + 3) + 5)| - 1) - 1) and g(x) = 3(-2sin(3π(2|x - 2| + 1) - 3) + 2)^2 - 2 from x = -0.1 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0044 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2(3sin(1π(-4(3|x - 1| + 1)^2 - 4(3|x - 1| + 1) - 4) + 2) - 1), g(x) = (-1(-2e^(1(1x^2 + 5x - 3)) + 2) + 3)/(-1(-2e^(1(1x^2 + 5x - 3)) + 2) + 3), x = 1.9, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0045 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2(3(2|x + 3| - 2) + 3)^2 - 5(3(2|x + 3| - 2) + 3) + 1 and g(x) = 2|((-2x - 2)/(-2x + 3)) + 1| + 1 from x = -4.0 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0046 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(1(-2|x + 1| - 1)) and g(x) = -1|x - 3| + 2 between the vertical lines x = 1.0 and x = 5.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 4.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0047 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (3(-1(3e^(-2(-2|x + 2| - 2)) + 1)^2 - 2(3e^(-2(-2|x + 2| - 2)) + 1)) - 2)/(2(-1(3e^(-2(-2|x + 2| - 2)) + 1)^2 - 2(3e^(-2(-2|x + 2| - 2)) + 1)) - 3), g(x) = 2((-1(1x - 1) + 2)/(1(1x - 1) - 3))^2 - 3((-1(1x - 1) + 2)/(1(1x - 1) - 3)), x = 2.4, and x = 3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0048 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1|(-4x - 3) + 3| - 3 and g(x) = -1x^2 + 1x + 1 from x = -0.7 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0049 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-4(4x - 1)^2 + 1(4x - 1) + 3) + 3| and g(x) = -2(-4x - 1)^2 - 4(-4x - 1) between the vertical lines x = 0.5 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0050 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 5(1(-3|(2e^(-1x) - 1) - 1| + 3)^2 - 4(-3|(2e^(-1x) - 1) - 1| + 3) - 4) - 5, g(x) = (-2(3|(5x - 5) - 2| - 2) + 3)/(3(3|(5x - 5) - 2| - 2) + 1), x = 1.3, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0051 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(-3|(2x - 4) + 3| + 1) + 1)/(-2(-3|(2x - 4) + 3| + 1)) and g(x) = 3|(-1x^2 + 3x - 2)| - 2 from x = 0.3 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 4.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0052 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(-1(-1|x|)^2 + 1(-1|x|) - 3) + 3)/(-2(-1(-1|x|)^2 + 1(-1|x|) - 3) - 1) and g(x) = -2|(1sin(1πx - 2)) - 2| + 3 from x = -2.7 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0053 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-1(-2sin(1π(4x - 3) + 2) - 2) - 3)/(3(-2sin(1π(4x - 3) + 2) - 2) - 1), g(x) = (-3(-4x - 5))/(-1(-4x - 5) - 1), x = -2.0, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0054 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3|((2x - 3)/(2x + 2))| + 2, g(x) = (-3x - 3)/(-1x - 3), x = 1.2, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0055 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -5(-2sin(1πx - 2) + 1) - 3, g(x) = 3x, x = -2.4, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 9.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0056 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-3(-5x) + 3)/(-1(-5x) + 2), g(x) = -1x - 1, x = -4.2, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 28.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0057 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2e^(-1x) - 2) - 3)/(-2(2e^(-1x) - 2) - 1) and g(x) = -4x + 1 between the vertical lines x = -0.2 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 25.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0058 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3|((3x - 2)/(3x + 1)) + 3|, g(x) = (-2x + 2)/(-3x - 1), x = -0.2, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0059 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1|(-2cos(2πx + 1) - 3) - 3| + 1, g(x) = 5x - 5, x = -0.3, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0060 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1sin(3π(-5x^2 - 3x + 4) - 1) + 3 and g(x) = (-3x - 3)/(2x + 1) from x = -0.7 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0061 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2|(2e^(1x) + 1)| - 2) + 3 and g(x) = 2sin(1π(5x + 5) - 2) - 2 between the vertical lines x = -1.2 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0062 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2cos(3π(-5(4(1|x + 2| - 3)^2) + 1) - 2) and g(x) = -5(-1|((2x - 3)/(-2x + 3)) - 1| + 2)^2 - 1(-1|((2x - 3)/(-2x + 3)) - 1| + 2) - 1 from x = -3.0 to x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0063 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -5(-1(-1|((-3x + 3)/(-3x)) + 2| + 3) - 1)^2 - 3(-1(-1|((-3x + 3)/(-3x)) + 2| + 3) - 1) + 5, g(x) = -2|(-1sin(3π(2x + 5) + 3) - 3)| - 2, x = 0.1, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0064 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -5(2x - 2)^2 - 1(2x - 2) + 1 and g(x) = -5x^2 - 5x - 4 from x = 0.3 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 25.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0065 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-2e^(1((-3(-2|x + 2| + 1) - 1)/(1(-2|x + 2| + 1) - 3))) + 3)^2 - 2(-2e^(1((-3(-2|x + 2| + 1) - 1)/(1(-2|x + 2| + 1) - 3))) + 3) - 4 and g(x) = 3e^(2(-2|(5x + 4)| + 1)) + 2 between the vertical lines x = -3.0 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0066 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(1π(5x^2 - 4x) - 1) + 2 and g(x) = -1x between the vertical lines x = -3.9 and x = -3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0067 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2((-3(2|x + 3|) + 1)/(2(2|x + 3|) + 1))^2 + 3((-3(2|x + 3|) + 1)/(2(2|x + 3|) + 1)) + 4 and g(x) = (1(-2sin(1πx + 1) + 1) + 1)/(-1(-2sin(1πx + 1) + 1) + 3) from x = 3.5 to x = 4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 4.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0068 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2cos(2π(-2|x + 1|) + 2) - 1, g(x) = (3x - 2)/(-2x - 3), x = 3.8, and x = 4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0069 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4(-1(3|(2e^(2x) - 1) - 2| + 2) + 4)^2 - 2(-1(3|(2e^(2x) - 1) - 2| + 2) + 4) and g(x) = (-3(-2(2|x - 1| - 2)^2 + 1(2|x - 1| - 2)) + 3)/(-2(-2(2|x - 1| - 2)^2 + 1(2|x - 1| - 2))) from x = -0.2 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0070 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1(-1|(-3(-2e^(-1x) - 2)^2 - 4(-2e^(-1x) - 2) + 2) - 2| - 1) and g(x) = 2(3|(5x^2 - 4x - 3)| + 2) + 5 from x = 0.1 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 10.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0071 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(1(1(-1|x + 3| + 1) + 4)^2 - 4(1(-1|x + 3| + 1) + 4) - 5) - 1)/(3(1(1(-1|x + 3| + 1) + 4)^2 - 4(1(-1|x + 3| + 1) + 4) - 5) + 3) and g(x) = -4(-2sin(2π((3x)/(3x - 2)) - 2) - 2)^2 - 2(-2sin(2π((3x)/(3x - 2)) - 2) - 2) + 5 between the vertical lines x = -0.2 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0072 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(3π(1x - 5) - 1) - 2 and g(x) = 2x^2 - 4x - 2 between the vertical lines x = 1.6 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0073 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2π(2x - 3) - 2) - 1 and g(x) = -3|x - 2| + 3 between the vertical lines x = 3.3 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0074 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 4(-4x^2 - 4x + 3) + 2 and g(x) = 4x^2 + 4x + 4 from x = -1.4 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 17.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0075 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1(-1|(1e^(-1(1x - 2)) - 3) - 2| - 3)^2 + 4(-1|(1e^(-1(1x - 2)) - 3) - 2| - 3) - 3 and g(x) = 5((-1(3x + 3) + 3)/(-2(3x + 3) + 3))^2 - 4((-1(3x + 3) + 3)/(-2(3x + 3) + 3)) + 3 from x = 0.0 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 4.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0076 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(-3|(-3cos(2πx - 1) + 2) - 1| - 3) + 2)/(-3(-3|(-3cos(2πx - 1) + 2) - 1| - 3)) and g(x) = -3cos(2π(1x^2 + 1x - 5)) - 3 from x = -3.1 to x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0077 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-2(-1e^(2x) - 2) - 2)/(-3(-1e^(2x) - 2)), g(x) = 1|x + 3|, x = -3.3, and x = -2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0078 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(-2|(3(-2sin(1πx + 2) - 1)^2 - 1(-2sin(1πx + 2) - 1)) - 1| + 3) - 1)/(-1(-2|(3(-2sin(1πx + 2) - 1)^2 - 1(-2sin(1πx + 2) - 1)) - 1| + 3) + 3) and g(x) = 3((2(-4x^2 - 3x + 4) + 2)/(-2(-4x^2 - 3x + 4) + 1)) - 2 from x = -1.5 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 33.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0079 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(2x) + 3)/(-2(2x)) and g(x) = (-2x)/(-3x + 2) from x = -0.6 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 12.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0080 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3(-1(-2|((2x - 2)/(-2x + 3)) - 2| - 1)^2 - 4(-2|((2x - 2)/(-2x + 3)) - 2| - 1) - 5) + 3, g(x) = 5(-1cos(1π((-3x - 3)/(-2x - 1)) - 3))^2 + 2(-1cos(1π((-3x - 3)/(-2x - 1)) - 3)) + 4, x = 1.2, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0081 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1((3x - 1)/(3x + 2)) - 1 and g(x) = 5x - 2 from x = -0.4 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0082 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1sin(1π((-2x - 3)/(3x - 1)) - 3) + 2 and g(x) = 4x^2 - 1x - 3 from x = -0.9 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 7.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0083 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1|((-1(2sin(2π(4x^2 + 1x - 2) - 3) + 3) - 1)/(-2(2sin(2π(4x^2 + 1x - 2) - 3) + 3) + 3)) + 3| - 1, g(x) = 2((-1(1|x + 2| - 2))/(-2(1|x + 2| - 2) + 3)) + 5, x = -4.9, and x = -4.800000000000001. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0084 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-3(-1|x - 3|) - 2)/(3(-1|x - 3|) - 1) and g(x) = -1x^2 + 1x + 4 from x = -1.8 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 14.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0085 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-1x^2 + 5x + 5))/(-2(-1x^2 + 5x + 5) + 3) and g(x) = -1|x - 1| between the vertical lines x = -0.5 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0086 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3sin(3π(2(-2|x + 1|) - 3) - 3) - 1, g(x) = (3(-2x + 4) - 1)/(2(-2x + 4) - 3), x = -1.0, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0087 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (2(1|(2(2cos(2πx + 3)) + 3)| + 3) + 3)/(-1(1|(2(2cos(2πx + 3)) + 3)| + 3)), g(x) = -1|(1(-1cos(2πx - 3) - 3)^2 + 2(-1cos(2πx - 3) - 3) + 3) + 2| + 3, x = -4.2, and x = -3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0088 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(1sin(3πx - 2) - 2) + 2| and g(x) = -5x + 5 between the vertical lines x = 1.3 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0089 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2cos(2π(5x^2 - 3x - 3) + 3) - 1 and g(x) = -5x + 5 from x = 1.2 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0090 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1π(-1((-3x + 2)/(3x + 3)) + 4)) - 2 and g(x) = 1((-1x)/(3x - 2))^2 + 3((-1x)/(3x - 2)) - 3 between the vertical lines x = -1.1 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0091 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (3(-1cos(3πx - 2) + 2) - 3)/(1(-1cos(3πx - 2) + 2)), g(x) = 1x + 2, x = -1.7, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0092 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2|(1cos(2πx - 1) - 1) + 2| + 1 and g(x) = -1x^2 - 3x + 3 from x = -3.4 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0093 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3cos(2π(2x + 4) - 1) - 3, g(x) = (2x + 1)/(2x - 3), x = 0.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0094 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((1x)/(2x + 1))^2 + 3((1x)/(2x + 1)) + 1 and g(x) = -2|x - 3| + 1 between the vertical lines x = -0.6 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| -5.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0095 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2cos(2π((2x - 3)/(1x + 1)) - 1) - 1 and g(x) = (-2x + 3)/(-1x) from x = 0.9 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0096 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2(-2sin(3πx - 3) + 2)^2 - 5(-2sin(3πx - 3) + 2), g(x) = -3x - 2, x = 3.3, and x = 3.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 8.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0097 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1(2|(5((-3x - 3)/(-3x + 4)) - 1) + 2| - 3)^2 - 5(2|(5((-3x - 3)/(-3x + 4)) - 1) + 2| - 3) - 2 and g(x) = (-3(3|(2x + 1) - 3| - 3) + 1)/(3(3|(2x + 1) - 3| - 3) + 2) from x = -0.2 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0098 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(1x^2 + 3x - 3) + 3)/(2(1x^2 + 3x - 3) + 3) and g(x) = -3x^2 - 3x - 5 from x = -3.4 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 34.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0099 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3|((3(-2sin(3πx - 2) + 2) - 3)/(-2(-2sin(3πx - 2) + 2) - 2)) + 1| - 3, g(x) = 4((3x)/(-3x - 3)), x = 1.3, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
End of preview. Expand
in Data Studio
Explorative Math Problems
This dataset contains explorative mathematical problem settings in paper "OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization" that assess whether a model can faithfully extend a single reasoning strategy beyond the range of complexities seen during training.
Overview
Exploratory generalization assesses whether a model can faithfully extend a single reasoning strategy beyond the range of complexities seen during training. Concretely, the model is exposed to problems drawn from one template, all lying within a "low-complexity" regime, and is then evaluated on harder instances from the same family. This axis probes robustness: does the model generalize the same algorithm to higher complexity problems? or does it merely memorize solutions at a fixed difficulty level?
Each explorative setting consists of:
- Training Dataset: Low-complexity problems from a specific mathematical domain
- Test In-Distribution: Problems of similar complexity to training data (test-in)
- Test Out-of-Distribution: Higher complexity problems from the same domain/template (test-out)
Quick Start
from datasets import load_dataset
# Load all explorative settings
dataset = load_dataset("allenai/omega-explorative")
# Load a specific explorative setting with all splits
func_area_data = load_dataset("allenai/omega-explorative", "algebra_func_area")
train_data = func_area_data["train"] # Low complexity training problems
test_in_data = func_area_data["test_in"] # Similar complexity test problems
test_out_data = func_area_data["test_out"] # Higher complexity test problems
# Load just specific splits
train_only = load_dataset("allenai/omega-explorative", "algebra_func_area", split="train")
test_out_only = load_dataset("allenai/omega-explorative", "algebra_func_area", split="test_out")
Dataset Description
Each explorative setting provides three splits to evaluate different aspects of generalization:
- Train: Low-complexity problems used for training/few-shot learning
- Test-in: Problems of similar complexity to training data (in-distribution evaluation)
- Test-out: Higher complexity problems from the same template (out-of-distribution evaluation)
The key challenge is whether models can extend the same reasoning strategy from low-complexity training problems to higher-complexity test problems in the same domain.
Citation
If you use this dataset, please cite the original work:
@article{sun2024omega,
title = {OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization},
author = {Yiyou Sun and Shawn Hu and Georgia Zhou and Ken Zheng and Hannaneh Hajishirzi and Nouha Dziri and Dawn Song},
journal = {arXiv preprint arXiv:2506.18880},
year = {2024},
}
Related Resources
- Transformative Dataset: See omega-transformative for transformative reasoning challenges
- Compositional Dataset: See omega-compositional for compositional reasoning challenges
- Paper: See the full details in paper
- Code Repository: See generation code on github
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