id
string | setting_key
string | messages
list | ground_truth
string | dataset
string |
|---|---|---|---|---|
algebra_func_area_train_0100 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 4(2sin(2π(3x^2 - 4x + 5) + 1) - 1) - 2 and g(x) = -3sin(1π(-3|x + 1| - 2)) - 2 from x = -1.1 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0101 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(2|(-4((1x - 1)/(3x - 2)) - 2)|)^2 - 3(2|(-4((1x - 1)/(3x - 2)) - 2)|) + 2 and g(x) = (1(-1cos(1π(3x^2 + 1x + 3) + 1) + 3))/(-1(-1cos(1π(3x^2 + 1x + 3) + 1) + 3) + 2) from x = 2.8 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 12.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0102 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-1|(3((1x - 2)/(-2x)) - 4) - 1| - 1)^2 - 2(-1|(3((1x - 2)/(-2x)) - 4) - 1| - 1) + 4 and g(x) = -3e^(1(-4((2x)/(-1x + 2))^2 + 1((2x)/(-1x + 2)) + 2)) - 2 between the vertical lines x = 0.4 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0103 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(-2(2|(-4x + 1)| - 2)^2 + 3(2|(-4x + 1)| - 2) + 4) - 3)/(-1(-2(2|(-4x + 1)| - 2)^2 + 3(2|(-4x + 1)| - 2) + 4) + 3) and g(x) = 1(2|((-3x + 3)/(-1x)) + 3| + 3) + 5 from x = 0.5 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0104 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(1cos(1π(-3x - 1) + 2) - 3) - 3)/(3(1cos(1π(-3x - 1) + 2) - 3) + 2) and g(x) = 1|(-5x^2 - 1x + 2) + 3| - 3 between the vertical lines x = -1.5 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0105 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(2e^(1x)) - 2| - 1 and g(x) = 1x^2 + 4x - 3 between the vertical lines x = -2.6 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0106 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 5((-2(1sin(1πx - 1) + 1) + 2)/(-1(1sin(1πx - 1) + 1) - 1))^2 + 1((-2(1sin(1πx - 1) + 1) + 2)/(-1(1sin(1πx - 1) + 1) - 1)) - 3, g(x) = -3(-5x^2 - 4x + 5) + 5, x = -1.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 17.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0107 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1sin(1π((-2(1|(-1x + 4) - 1| - 1) - 1)/(-3(1|(-1x + 4) - 1| - 1) - 3)) - 3) - 3 and g(x) = -3|(-2cos(1π(5x^2 + 1x - 2) + 2) - 3) + 2| + 3 from x = -1.9 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0108 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3((1(2(-3|x|)^2 - 1(-3|x|) - 4) - 2)/(3(2(-3|x|)^2 - 1(-3|x|) - 4) + 3)) - 4, g(x) = 1sin(2π(1(1x^2 - 2x - 2) - 1) + 2) + 2, x = -0.3, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0109 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-1(2cos(2π(3|x + 1| + 2) - 2) + 2) + 2)/(1(2cos(2π(3|x + 1| + 2) - 2) + 2) + 3), g(x) = 5((-1x - 1)/(-1x + 3)) - 2, x = -3.5, and x = -3.4. 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_0110 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 5(-2|((3x - 2)/(3x + 3)) + 2| - 1)^2 + 5(-2|((3x - 2)/(3x + 3)) + 2| - 1) and g(x) = 2(1cos(1πx - 1) + 3) + 2 from x = -0.5 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0111 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3sin(3π((-2(-1x - 4) + 1)/(-3(-1x - 4) + 4)) + 2) - 3, g(x) = -2e^(-1(-1x - 2)), x = -4.6, and x = -4.5. 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_0112 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3sin(1π(4(-3x + 4)^2 + 2(-3x + 4) - 4) - 3) + 1, g(x) = 2|(-1e^(2x) - 1) - 2| - 3, x = -4.5, and x = -4.4. 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_0113 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((2(-2x^2 - 1x + 5) + 1)/(1(-2x^2 - 1x + 5) - 2)) + 1 and g(x) = (-2(-1|x + 1| - 1))/(-3(-1|x + 1| - 1) - 2) between the vertical lines x = -1.9 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 34.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0114 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(1sin(2πx - 1)) + 1)/(3(1sin(2πx - 1)) - 1) and g(x) = -3|x - 1| - 3 from x = 2.2 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0115 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1(5((-3(-1|x - 1| - 3) + 1)/(-2(-1|x - 1| - 3) - 3)) - 3)^2 - 2(5((-3(-1|x - 1| - 3) + 1)/(-2(-1|x - 1| - 3) - 3)) - 3) + 5, g(x) = -2|(3((1x - 3)/(3x + 1))^2 - 3((1x - 3)/(3x + 1)) + 1) - 2| - 1, x = -0.6, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| -84.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0116 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4(2(1sin(3πx - 3) + 1) - 3)^2 + 3(2(1sin(3πx - 3) + 1) - 3) + 3 and g(x) = -2(2x - 5)^2 - 1(2x - 5) + 3 from x = 2.5 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0117 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3cos(2π(-1x^2 - 3x - 2) - 2) - 1 and g(x) = -2x^2 + 2x - 3 from x = 1.3 to x = 1.4000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0118 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1|(4(-5((-2x - 2)/(2x - 3))^2 + 2((-2x - 2)/(2x - 3)) + 5) - 1) + 2| - 2, g(x) = 1((-1(-1|x - 2| + 1) - 2)/(1(-1|x - 2| + 1))) + 4, x = 0.3, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0119 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3(-2sin(2π((-1(-1|x + 3|) + 3)/(-3(-1|x + 3|) - 2)) - 2) - 1)^2 + 2(-2sin(2π((-1(-1|x + 3|) + 3)/(-3(-1|x + 3|) - 2)) - 2) - 1), g(x) = 5((-3(-2cos(3πx - 3)) + 3)/(1(-2cos(3πx - 3))))^2 + 3((-3(-2cos(3πx - 3)) + 3)/(1(-2cos(3πx - 3)))), x = -2.1, and x = -2.0. 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_0120 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -4(-1sin(2πx - 1)) - 3, g(x) = -2|x + 1| - 2, x = 0.8, and x = 1.0. 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_0121 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2sin(1π(3x^2 + 1x - 1) + 2) + 1 and g(x) = -4x + 2 from x = 0.2 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0122 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3((-2x - 1)/(3x + 2))^2 + 1((-2x - 1)/(3x + 2)) + 4 and g(x) = (1x + 3)/(2x - 1) from x = -0.9 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| -0.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0123 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3|(-3(-4((-3x - 3)/(-2x + 3))^2 + 5((-3x - 3)/(-2x + 3)) - 1) + 4) - 2| - 1 and g(x) = 2sin(3π(3|(-1x^2 - 5x + 4) - 2| + 2) - 3) from x = -4.3 to x = -4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0124 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (1(-5(-5x^2 + 4x + 4) - 3) - 3)/(2(-5(-5x^2 + 4x + 4) - 3) + 1), g(x) = 3(1cos(3πx - 2) + 1)^2 - 1(1cos(3πx - 2) + 1), x = 2.4, 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_0125 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-3(3cos(3πx - 1)) + 2)/(2(3cos(3πx - 1)) - 1) and g(x) = (2x - 2)/(2x) from x = 2.0 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0126 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(1|((-1(-2sin(2πx + 2) - 2) - 1)/(-1(-2sin(2πx + 2) - 2) + 3)) + 2|) - 1 and g(x) = -4(2((-1x)/(-3x - 1))^2 - 5((-1x)/(-3x - 1)) - 1) + 3 between the vertical lines x = -0.4 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| -4.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0127 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (1(2(-2|(-4x^2 + 3x + 2) + 2| + 3) - 2) - 3)/(-2(2(-2|(-4x^2 + 3x + 2) + 2| + 3) - 2) + 3) and g(x) = -4(1|(1x^2 - 5x + 4) - 1|) - 3 from x = 1.4 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0128 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3|x - 3| - 3) - 3 and g(x) = -4x^2 - 3x + 4 between the vertical lines x = -0.5 and 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_0129 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3cos(3π(3|(4(-3x - 5)^2 + 5(-3x - 5) + 5) - 1| - 2) + 3) + 1, g(x) = -1cos(3π(-2|(1x^2 + 2x + 2) + 2|) - 2) + 1, x = -2.1, and x = -2.0. 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_0130 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1sin(2π(2((3(-3|x + 1| + 2) - 1)/(-3(-3|x + 1| + 2) + 4))^2 - 4((3(-3|x + 1| + 2) - 1)/(-3(-3|x + 1| + 2) + 4)) + 1) + 1) + 2, g(x) = -2|((-3(2x^2 - 3x + 5) - 1)/(-3(2x^2 - 3x + 5) + 4)) - 1| + 2, x = -0.9, and x = -0.8. 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_0131 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-2sin(2π(-1|(-1x - 2) - 1| + 1) - 3) + 2)^2 - 5(-2sin(2π(-1|(-1x - 2) - 1| + 1) - 3) + 2) + 4 and g(x) = (2(-3(-1x^2 - 5x - 1) + 4) + 2)/(2(-3(-1x^2 - 5x - 1) + 4) - 1) between the vertical lines x = 2.2 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0132 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1((-1(-3|x + 1| + 3) - 3)/(3(-3|x + 1| + 3) - 2)) + 4, g(x) = 2|(-3e^(2x) - 2) + 3| + 3, x = -2.1, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 15.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0133 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2cos(1π(5x - 2)) + 3, g(x) = -4x - 4, x = -2.1, and x = -1.9. 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_0134 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -5(-2|x| + 2)^2 + 5(-2|x| + 2) + 1, g(x) = 5x + 4, x = -1.2, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0135 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4((3(2|(-5x - 2) + 2| + 1) - 3)/(-1(2|(-5x - 2) + 2| + 1) + 2))^2 - 5((3(2|(-5x - 2) + 2| + 1) - 3)/(-1(2|(-5x - 2) + 2| + 1) + 2)) + 2 and g(x) = 3((1(-1sin(1πx) + 1) + 1)/(-3(-1sin(1πx) + 1) + 1)) from x = 2.2 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 32.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0136 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-2e^(-1(1|(-1x^2 - 5x) + 1| - 1)) + 2) + 1 and g(x) = 2(-1((1x - 2)/(2x + 1))^2 - 2((1x - 2)/(2x + 1)) + 3) + 2 between the vertical lines x = -4.9 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 33.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0137 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(4(1|(-4x - 4) + 1| - 1)^2 + 3(1|(-4x - 4) + 1| - 1) + 5) - 3)/(-2(4(1|(-4x - 4) + 1| - 1)^2 + 3(1|(-4x - 4) + 1| - 1) + 5) + 1) and g(x) = (2(4(-2|x - 1| + 1) + 2) - 3)/(3(4(-2|x - 1| + 1) + 2) - 2) between the vertical lines x = 0.4 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0138 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2sin(1π(-4((-1(3|x + 2| - 3) - 3)/(-1(3|x + 2| - 3) + 2)) + 3) - 2) - 3, g(x) = -3(-4((2x - 2)/(-1x + 3))^2 - 4((2x - 2)/(-1x + 3)) + 2) - 5, x = -3.6, and x = -3.5. 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_0139 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((3(-2e^(1x) - 3) - 3)/(-1(-2e^(1x) - 3) - 2)) + 1 and g(x) = -2((-1x - 2)/(2x))^2 + 4((-1x - 2)/(2x)) - 3 between the vertical lines x = -0.2 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| -26.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0140 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1(5x^2 - 4x - 2) + 4 and g(x) = -3x + 1 from x = -0.5 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 12.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0141 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(3π(3x^2 - 1x - 1) - 2) - 2 and g(x) = (2x + 2)/(-2x + 3) between the vertical lines x = 4.2 and x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0142 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1cos(2π(-1(-2|(-1x^2 - 4x - 5)| - 2) - 4) - 2) + 2, g(x) = 3(1cos(2π((-1x - 1)/(2x - 1)) + 1) - 1) + 3, x = -4.1, and x = -3.9999999999999996. 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_0143 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-2(1(-1|x - 3| - 2) + 3) - 3)/(-1(1(-1|x - 3| - 2) + 3)) and g(x) = -3(-2cos(1πx - 2) + 2)^2 + 3(-2cos(1πx - 2) + 2) + 3 from x = 1.1 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 13.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0144 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-3(1x^2 - 2x - 3) + 1)/(-2(1x^2 - 2x - 3) - 3) and g(x) = -1x + 4 from x = 1.4 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 13.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0145 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(2((-2(-2x + 5) - 2)/(2(-2x + 5) + 3))^2 + 1((-2(-2x + 5) - 2)/(2(-2x + 5) + 3)) - 2) - 1| - 1 and g(x) = -3|(-5(-2cos(2πx - 1) - 3)^2 + 4(-2cos(2πx - 1) - 3) + 4) - 3| + 1 between the vertical lines x = 3.2 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 46.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0146 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1(1cos(1π(1((-2x - 1)/(-3x - 3)) - 1) - 2) - 3)^2 + 2(1cos(1π(1((-2x - 1)/(-3x - 3)) - 1) - 2) - 3) + 3 and g(x) = 3|(-1((1x)/(3x - 1))^2 + 5) - 1| + 1 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| -3.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0147 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3cos(1π(4x^2 + 4x - 4) - 2) + 3, g(x) = (1x - 1)/(1x + 1), x = -4.9, and x = -4.8. 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_0148 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(-1|(-2cos(3π(-1x^2 + 1x + 1) - 3) + 3) + 1| - 3) + 3)/(-1(-1|(-2cos(3π(-1x^2 + 1x + 1) - 3) + 3) + 1| - 3)) and g(x) = (-1(1e^(2(-2x^2 + 5x + 4)) - 3) - 1)/(-2(1e^(2(-2x^2 + 5x + 4)) - 3) - 3) from x = -0.6 to x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0149 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (2(2(1|(1x - 2) - 3| - 2)^2 - 5) + 2)/(3(2(1|(1x - 2) - 3| - 2)^2 - 5) + 1), g(x) = (-1(3sin(1π(2x^2 - 1x + 5) - 1) - 3) - 1)/(-1(3sin(1π(2x^2 - 1x + 5) - 1) - 3) + 3), x = 1.9, and x = 2.1. 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_0150 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1((1x)/(1x + 2))^2 + 5((1x)/(1x + 2)) - 2, g(x) = 1x - 3, x = -0.4, and x = 3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 4.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0151 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((-3x + 1)/(-1x + 2))^2 - 5((-3x + 1)/(-1x + 2)) - 2 and g(x) = -3x^2 + 3x - 2 between the vertical lines x = 0.4 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0152 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-3|(3x^2 - 3x + 5)| - 1) - 3)/(-2(-3|(3x^2 - 3x + 5)| - 1) + 3) and g(x) = (1(-4x^2 - 5x + 3) - 3)/(-2(-4x^2 - 5x + 3) - 3) between the vertical lines x = -2.1 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 6.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0153 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-4((3(3sin(3πx - 2) - 1) + 3)/(-2(3sin(3πx - 2) - 1) + 3)) - 1) - 1| and g(x) = -1(-2sin(3π(-3x - 2) + 3) + 3)^2 - 3(-2sin(3π(-3x - 2) + 3) + 3) - 2 between the vertical lines x = -4.3 and x = -4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 38.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0154 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3(5x^2 - 5) - 1 and g(x) = 5x + 1 from x = -0.9 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 25.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0155 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(3|x + 3| - 2) + 1)/(1(3|x + 3| - 2) + 3) and g(x) = -1|x + 1| between the vertical lines x = -1.6 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0156 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1(3(-3|x + 2| + 2) + 2)^2 + 3(3(-3|x + 2| + 2) + 2) + 4, g(x) = 2|(2sin(1πx - 3) + 2) + 3| - 1, x = -1.4, and x = -1.3. 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_0157 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 4(1|((3x + 1)/(-3x - 3)) - 2|)^2 + 2(1|((3x + 1)/(-3x - 3)) - 2|) - 3 and g(x) = 2|(-2x^2 + 4x + 4) - 1| + 1 from x = -0.8 to x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0158 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-1|(2x^2 - 2x - 2) + 2| + 2) + 3)/(-1(-1|(2x^2 - 2x - 2) + 2| + 2) + 2) and g(x) = -4(3x^2 + 1x - 3) - 3 between the vertical lines x = -1.1 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0159 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(-1(-5(2(-2|x - 3| + 3) - 4)^2 + 5(2(-2|x - 3| + 3) - 4) - 1)) + 1 and g(x) = -4(-4((-3x + 3)/(-1x - 3)) + 5)^2 - 4(-4((-3x + 3)/(-1x - 3)) + 5) + 3 between the vertical lines x = 2.4 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 4.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0160 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(-1cos(1π((-2(-3|x - 2| - 3) + 3)/(-2(-3|x - 2| - 3) - 3)) + 1) - 3)^2 - 1(-1cos(1π((-2(-3|x - 2| - 3) + 3)/(-2(-3|x - 2| - 3) - 3)) + 1) - 3) - 4 and g(x) = (-2(-4(-2|x + 3|)^2 - 1(-2|x + 3|) + 4) + 1)/(-1(-4(-2|x + 3|)^2 - 1(-2|x + 3|) + 4) - 3) from x = -3.7 to x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 26.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0161 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(3|x - 1|) - 2)/(-2(3|x - 1|) - 2) and g(x) = (3x - 2)/(1x) from x = 0.7 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0162 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(5((2x)/(-1x + 2))^2 + 5) - 1| and g(x) = (-3(-2|x + 3| + 2) + 2)/(-2(-2|x + 3| + 2) + 1) between the vertical lines x = -3.8 and x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 35.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0163 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-3(-5(-2x^2 - 5x - 4)) - 3)/(1(-5(-2x^2 - 5x - 4)) - 2), g(x) = (-2(3x^2 + 5x - 4) + 2)/(3(3x^2 + 5x - 4) - 2), x = -2.3, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 11.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0164 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3((-3(-2cos(2π(-2x^2 - 2x + 4) - 3) + 1) - 2)/(-1(-2cos(2π(-2x^2 - 2x + 4) - 3) + 1))), g(x) = -2(2e^(-2(1|x - 2| + 1)) - 3) - 4, x = 4.5, and x = 4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0165 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (1(1|(2(-4x + 3)^2) + 1| - 3) + 2)/(3(1|(2(-4x + 3)^2) + 1| - 3) - 2), g(x) = (-2(2|(1cos(1πx + 3) - 3) - 2| - 2) - 3)/(-3(2|(1cos(1πx + 3) - 3) - 2| - 2)), x = 0.4, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0166 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1sin(3π(4x + 1) - 3), g(x) = (3x - 2)/(-2x + 3), x = -0.5, 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_0167 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2cos(2π(3x + 5) + 2), g(x) = (-2x + 3)/(-1x + 2), x = 0.2, and x = 0.3. 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_0168 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1|((-3(2(-2x^2 - 1x + 2) + 4) - 2)/(3(2(-2x^2 - 1x + 2) + 4) + 3))| - 2, g(x) = -1sin(1π(1((-3x)/(2x + 3))^2 - 1((-3x)/(2x + 3)) - 2) + 2), x = -2.6, and x = -2.5. 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_0169 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3(2|x - 2| + 1)^2 + 2(2|x - 2| + 1) - 3 and g(x) = 2x from x = 1.9 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0170 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(1|(3sin(3π(-4x^2 + 3x - 1) + 2) + 2) + 1| + 2) + 3)/(-3(1|(3sin(3π(-4x^2 + 3x - 1) + 2) + 2) + 1| + 2)) and g(x) = -2(-2(-3|x - 3| - 1)^2 + 1(-3|x - 3| - 1) + 5) + 2 between the vertical lines x = 3.0 and x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0171 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(2cos(2π((-1x - 3)/(1x + 2)) + 3) + 2) + 5 and g(x) = 3|(4x^2 - 5x) - 3| + 2 between the vertical lines x = 0.2 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0172 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2cos(1π((-3x + 1)/(-1x))) + 1, g(x) = (-3x + 2)/(-2x - 3), x = -0.1, and x = 0.0. 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_0173 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(4x^2 + 5x - 3) - 1)/(1(4x^2 + 5x - 3)) and g(x) = -2x^2 + 4x + 5 between the vertical lines x = 0.4 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 18.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0174 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2(1x^2 - 4) + 2 and g(x) = -5x^2 + 5x - 5 from x = -0.2 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0175 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3|(-1sin(1πx - 2) - 3) + 3| - 1 and g(x) = 3x^2 - 5x - 5 from x = -0.9 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 17.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0176 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2|(1x - 1) - 1| + 1 and g(x) = (1x + 2)/(1x + 3) from x = 1.9 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0177 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2e^(-1(2x - 1)) - 3 and g(x) = -1x^2 + 1x between the vertical lines x = 0.3 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0178 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-4x) - 1)/(-2(-4x) + 3) and g(x) = -2|x + 1| + 2 between the vertical lines x = -1.2 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0179 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -5((2(3|x + 1| - 1) - 3)/(2(3|x + 1| - 1) - 1))^2 + 3((2(3|x + 1| - 1) - 3)/(2(3|x + 1| - 1) - 1)) - 1, g(x) = -2(4x^2 + 1x + 2), x = -1.0, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| -5.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0180 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((2(-2|x + 2| + 2) + 3)/(-3(-2|x + 2| + 2) + 1)) - 5 and g(x) = 2sin(1π(1|x + 2| + 1) - 3) + 3 between the vertical lines x = -2.6 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 4.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0181 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-2(-4(1(-3|x + 2|)^2 - 1(-3|x + 2|) + 3) - 1) + 2)/(2(-4(1(-3|x + 2|)^2 - 1(-3|x + 2|) + 3) - 1) - 3), g(x) = 1(-1|((-2x + 3)/(-3x + 1)) - 2| - 3) + 5, x = 0.2, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 35.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0182 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(1π(-5(-2x^2 + 2x - 4) + 5) + 1) - 2 and g(x) = (-2(-2x^2 - 2x - 4))/(-3(-2x^2 - 2x - 4)) between the vertical lines x = 3.4 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0183 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3((2(5(-3|x - 1| - 2) - 1) - 1)/(-2(5(-3|x - 1| - 2) - 1)))^2 - 5((2(5(-3|x - 1| - 2) - 1) - 1)/(-2(5(-3|x - 1| - 2) - 1))) - 4 and g(x) = (-1(2(1x + 1)^2 + 3(1x + 1) - 3) + 1)/(-1(2(1x + 1)^2 + 3(1x + 1) - 3) - 2) from x = -3.0 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 24.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0184 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1|(2cos(2π(-1((3x)/(-3x + 4)) - 2) - 3) + 3) + 1| + 3, g(x) = 2|(-5(-3cos(1πx + 3) - 2)^2 + 1(-3cos(1πx + 3) - 2) - 2) - 2| - 3, x = 3.7, and x = 3.9. 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_0185 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(1|(3cos(2π(-5x - 5) - 1) - 3) + 1| + 2)^2 + 4(1|(3cos(2π(-5x - 5) - 1) - 3) + 1| + 2) + 5 and g(x) = (-1(1e^(1(1x^2 - 3x + 3)) - 3) + 3)/(2(1e^(1(1x^2 - 3x + 3)) - 3)) from x = -1.9 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0186 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(3x + 1) + 2)/(-3(3x + 1) + 1) and g(x) = -5x - 4 between the vertical lines x = -0.7 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 16.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0187 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1|((-2(-5(2x^2 - 4x + 1) - 3) - 2)/(-2(-5(2x^2 - 4x + 1) - 3) - 1)) - 1| + 2 and g(x) = 5((2(-1|x + 2| + 3) + 2)/(-2(-1|x + 2| + 3) - 2))^2 - 1((2(-1|x + 2| + 3) + 2)/(-2(-1|x + 2| + 3) - 2)) + 5 from x = 0.5 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 9.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0188 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (2(1(-3cos(2πx + 3) - 3)^2 - 2(-3cos(2πx + 3) - 3) + 1) + 3)/(1(1(-3cos(2πx + 3) - 3)^2 - 2(-3cos(2πx + 3) - 3) + 1) + 3), g(x) = (3(-2|x + 3| + 3) + 1)/(-3(-2|x + 3| + 3)), x = -4.6, and x = -1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 11.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0189 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2|(2x - 1) + 2| - 3, g(x) = -2x^2 - 3, x = -0.4, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 7.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0190 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1((1(-1cos(1πx)))/(-1(-1cos(1πx)) - 1)) - 2, g(x) = (-2(-1e^(1x) + 1) - 1)/(-2(-1e^(1x) + 1) + 3), x = -4.3, and x = -3.6. 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_0191 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(1(-1|(-2e^(1x)) + 3| + 2)^2 - 5(-1|(-2e^(1x)) + 3| + 2) - 5) - 4 and g(x) = 4(-3(-1|x + 1| + 1) - 4)^2 - 1(-3(-1|x + 1| + 1) - 4) - 2 from x = 0.7 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0192 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2cos(2π(-2(3|x - 3| - 1) - 4) + 1) - 1)^2 - 5(2cos(2π(-2(3|x - 3| - 1) - 4) + 1) - 1) + 1 and g(x) = (1(3e^(2(2|x + 2|)) + 2))/(2(3e^(2(2|x + 2|)) + 2) + 3) between the vertical lines x = 3.0 and x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0193 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(2sin(1π(-4x) - 2) - 3) - 3)/(-2(2sin(1π(-4x) - 2) - 3) - 3) and g(x) = -3|(2sin(2πx - 2)) - 1| - 2 from x = 0.3 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0194 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1|(-2cos(1πx - 1) + 1)| - 1 and g(x) = (3x)/(-1x + 2) from x = -3.6 to x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0195 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3e^(-2(-1|x|)) - 2, g(x) = 2x + 4, x = -0.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0196 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2e^(-1((-2(3x - 4) + 1)/(-2(3x - 4) - 3))) + 1, g(x) = -1|((2x - 1)/(1x)) + 2| + 2, x = 0.2, and x = 0.3. 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_0197 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3(-3|(-3e^(-2x) + 2) + 2| + 3) and g(x) = 2|((3x - 2)/(-1x + 3)) - 1| + 3 from x = 0.1 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 37.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0198 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(2|x + 1| - 3) + 2)/(-2(2|x + 1| - 3) + 3) and g(x) = -2x - 3 between the vertical lines x = -2.9 and x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0199 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1cos(3π(-3|((-1x - 1)/(-1x + 2))| - 2) - 3) + 3 and g(x) = -1(-2x^2 + 1) from x = 1.4 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
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