id
string | setting_key
string | messages
list | ground_truth
string | dataset
string |
|---|---|---|---|---|
algebra_func_area_train_0200 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-3(2cos(1πx + 2) - 1) + 2)/(2(2cos(1πx + 2) - 1) - 1) and g(x) = -4x - 1 from x = 1.1 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0201 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(5x^2 - 5) - 3)/(-3(5x^2 - 5) - 2) and g(x) = 2x - 1 from x = 0.0 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 8.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0202 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2cos(1π(-2x^2 + 4x - 1) - 3) + 1 and g(x) = -2x^2 - 2x - 1 from x = -0.9 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0203 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3cos(2π(-2|x|) + 3) and g(x) = -1x^2 + 3x + 3 from x = 4.2 to x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0204 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3|(1sin(3π(1x^2 - 1))) + 2| - 3 and g(x) = 2e^(-1(3x + 1)) - 1 from x = -0.6 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0205 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3(-1sin(3π(-2x - 3)))^2 + 2(-1sin(3π(-2x - 3))) + 4) - 1)/(1(3(-1sin(3π(-2x - 3)))^2 + 2(-1sin(3π(-2x - 3))) + 4)) and g(x) = (2(-2e^(-2(-2|x - 3| + 3)) - 2))/(-1(-2e^(-2(-2|x - 3| + 3)) - 2) + 2) 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}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0206 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3(1cos(2π(-2|((-1x - 1)/(1x + 2)) - 3| - 3) + 1) - 2)^2 - 3(1cos(2π(-2|((-1x - 1)/(1x + 2)) - 3| - 3) + 1) - 2) - 4 and g(x) = (-1(4(1cos(2πx) + 1)^2 - 1(1cos(2πx) + 1) + 1) - 1)/(1(4(1cos(2πx) + 1)^2 - 1(1cos(2πx) + 1) + 1) - 3) from x = -0.3 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 7.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0207 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1sin(2π(2|x - 1| - 2) - 1) + 3 and g(x) = 3|x - 3| + 2 from x = 3.1 to x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0208 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2e^(1(-1(2|(3x - 4) + 3| - 1)^2 - 1(2|(3x - 4) + 3| - 1) + 1)), g(x) = (2(-2(3x + 2)^2 - 3(3x + 2) + 4) - 3)/(3(-2(3x + 2)^2 - 3(3x + 2) + 4) + 2), x = 0.0, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0209 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1cos(1π(4((-2x - 3)/(2x - 3)) - 5) - 3) - 2 and g(x) = (3(2cos(3πx) - 3) + 2)/(-2(2cos(3πx) - 3) - 2) from x = 2.3 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0210 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2|((3(5x - 3) - 2)/(-3(5x - 3) - 1))| + 3 and g(x) = (1(3|x + 2| - 3) + 3)/(2(3|x + 2| - 3)) from x = -3.1 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 23.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0211 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1|(2sin(2πx - 1)) - 1| + 1, g(x) = (-2x - 2)/(2x), x = -0.4, and x = -0.2. 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_0212 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1|(2cos(3πx + 3) - 1) + 3| + 2 and g(x) = 1x^2 + 4x + 5 from x = -2.6 to x = -2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0213 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(3((-3(2|x| - 1) - 1)/(1(2|x| - 1) + 2))^2 - 4((-3(2|x| - 1) - 1)/(1(2|x| - 1) + 2)) - 3) + 4 and g(x) = 4(-2|(2x^2 - 5x + 4)| + 2) - 3 between the vertical lines x = 1.0 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 4.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0214 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-2|(2(-5x^2 + 2x) + 1) + 1|) + 3)/(3(-2|(2(-5x^2 + 2x) + 1) + 1|) + 1) and g(x) = -1(2((2x + 3)/(-3x - 3))^2 - 3((2x + 3)/(-3x - 3)) + 5) - 4 between the vertical lines x = 0.7 and x = 0.7999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0215 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1sin(2π((-3x - 2)/(1x - 2)) + 1) + 2 and g(x) = -3x + 3 from x = 0.5 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_0216 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -4(-1(1|x - 1| + 3)^2 + 3(1|x - 1| + 3) + 3) + 2, g(x) = 1sin(2π(-1|x - 2| + 2) + 1) + 3, x = 0.1, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 11.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0217 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3|((-2(3cos(3πx) + 2) + 1)/(1(3cos(3πx) + 2) + 3)) + 3| - 3 and g(x) = 4((1x - 3)/(-3x - 3))^2 - 5((1x - 3)/(-3x - 3)) + 3 from x = -3.7 to x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0218 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2e^(-2(-1|x - 2| + 3)) + 3 and g(x) = 2|x - 3| - 1 from x = 1.0 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 7.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0219 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1|((3(-3(2x^2 + 2x) + 1) - 1)/(3(-3(2x^2 + 2x) + 1) - 1)) + 2| - 2, g(x) = -2sin(1π(-1(2|x - 1| - 2)) - 3) + 1, x = -3.5, and x = -3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0220 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3|((1(-1x - 3) + 3)/(2(-1x - 3) - 3))| + 1, g(x) = (-2(3x^2 + 1x - 4) - 1)/(1(3x^2 + 1x - 4) + 2), x = -3.0, and x = -1.2. 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_0221 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4(-1sin(2π(1x + 4) + 1) + 1)^2 + 4(-1sin(2π(1x + 4) + 1) + 1) + 4 and g(x) = -2e^(1((-3x - 1)/(3x - 1))) - 2 from x = -1.5 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0222 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-1sin(2π(-4x^2 + 5x + 3) - 3) + 1) - 2| - 1 and g(x) = -3(-3x - 2)^2 + 5(-3x - 2) - 4 between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0223 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(-2cos(3πx - 2) + 2))/(-1(-2cos(3πx - 2) + 2) + 2) and g(x) = -2|x - 1| - 2 from x = 0.4 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0224 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3sin(3π(-1|x + 2| + 3) + 3) + 2, g(x) = (3x + 1)/(1x + 3), x = -0.3, and x = -0.1. 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_0225 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (3(5(3|(-5x^2 + 2x + 3) - 2|) - 3) + 3)/(2(5(3|(-5x^2 + 2x + 3) - 2|) - 3) - 1), g(x) = (3(-1|(2x - 2) + 3| + 1) + 2)/(1(-1|(2x - 2) + 3| + 1) + 1), x = -0.4, and x = -0.2. 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_0226 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(2sin(2π((-2x + 2)/(-2x - 1)) + 2) + 1)^2 - 4(2sin(2π((-2x + 2)/(-2x - 1)) + 2) + 1) + 4 and g(x) = (1(2x - 4) + 1)/(2(2x - 4) + 3) between the vertical lines x = -0.7 and 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_0227 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (1(-5(-2|(3cos(2πx + 2) - 1) + 1|)) - 3)/(1(-5(-2|(3cos(2πx + 2) - 1) + 1|))) and g(x) = -1|(3(-3x + 1)^2 + 5(-3x + 1) - 1) + 3| from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0228 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3|(3((3(5x - 2) - 1)/(-1(5x - 2) + 3))^2 + 2((3(5x - 2) - 1)/(-1(5x - 2) + 3)) - 2) - 3| - 3 and g(x) = (3(-1|(4x^2 - 5x) + 2| - 1) + 1)/(1(-1|(4x^2 - 5x) + 2| - 1) + 1) from x = 0.5 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0229 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -5(-1x + 2)^2 + 5(-1x + 2) - 3, g(x) = -1|x + 2| + 1, x = 1.2, 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_0230 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1e^(-2(3(1x + 5)^2 - 5(1x + 5) - 3)) + 1, g(x) = 2(-4x - 4)^2 - 3(-4x - 4) + 1, x = -1.4, and x = -1.0. 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_0231 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(4(-2|(-2x - 5) - 1| - 1)^2 - 5(-2|(-2x - 5) - 1| - 1) + 1))/(1(4(-2|(-2x - 5) - 1| - 1)^2 - 5(-2|(-2x - 5) - 1| - 1) + 1) + 2) and g(x) = -2e^(-1(-5(5x^2 + 3x - 4) + 4)) between the vertical lines x = -1.3 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0232 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3cos(2π(-2x - 4) + 2) + 1) - 1)/(-3(3cos(2π(-2x - 4) + 2) + 1) - 3) and g(x) = (2(-5x^2 - 5x + 3) + 2)/(1(-5x^2 - 5x + 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}"
}
]
| 8.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0233 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1|((1(2(-1x - 3)^2 - 2(-1x - 3) + 1) + 1)/(1(2(-1x - 3)^2 - 2(-1x - 3) + 1) + 3))| + 2, g(x) = 2|(2((1x - 3)/(3x))^2 + 4((1x - 3)/(3x)) + 1)|, x = 1.2, and x = 2.2. 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_0234 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1|((-2(-5x + 1) - 3)/(1(-5x + 1) - 3)) - 2|, g(x) = -1|(-5x^2 + 5x + 4) - 3| + 2, x = -0.1, and x = 0.1. 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_0235 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(2sin(1π(2|((-2x + 1)/(1x + 3))| - 2)) + 1)^2 - 3(2sin(1π(2|((-2x + 1)/(1x + 3))| - 2)) + 1) - 2 and g(x) = (-1(1(2x^2 + 2x + 1) - 2) + 3)/(2(1(2x^2 + 2x + 1) - 2) + 2) between the vertical lines x = -2.6 and x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0236 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1e^(2(3|(-1x - 2)| - 1)) - 2, g(x) = -1|(-1cos(3πx - 3) + 1) + 1| - 3, x = -2.5, and x = -1.5. 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_0237 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((2(-5(2|x + 1| + 1)^2 + 2(2|x + 1| + 1) - 2) + 3)/(-3(-5(2|x + 1| + 1)^2 + 2(2|x + 1| + 1) - 2) - 2)) + 1 and g(x) = 1((1(-1x^2 - 5x - 4) + 1)/(-1(-1x^2 - 5x - 4) - 2)) + 1 between the vertical lines x = -4.5 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 9.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0238 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1cos(2π(1|x + 1| + 2)) - 2, g(x) = -4x - 1, x = 0.2, and x = 0.5. 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_0239 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(1π(2x + 2) - 3) and g(x) = -2|x + 1| + 1 between the vertical lines x = -0.2 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0240 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3cos(3π(2|(1((-2x + 3)/(1x + 3))^2 + 5((-2x + 3)/(1x + 3)) + 4) + 3| - 2) + 3), g(x) = -1|(-3((-1x + 1)/(1x - 2)) - 2) - 2| + 1, x = -3.8, and x = -3.6999999999999997. 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_0241 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3|(-3x) - 1| + 1 and g(x) = 1x^2 - 2x - 3 from x = -0.6 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0242 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(2|x + 2| - 2) + 1)/(-2(2|x + 2| - 2) - 2) and g(x) = -2|x + 2| + 3 between the vertical lines x = -3.9 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0243 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2(2((2(-2|x + 2| + 3))/(3(-2|x + 2| + 3) - 2)))^2 - 4(2((2(-2|x + 2| + 3))/(3(-2|x + 2| + 3) - 2))) + 5 and g(x) = (-1(-3cos(1π(1x^2 + 4x - 1) - 3)) + 2)/(2(-3cos(1π(1x^2 + 4x - 1) - 3)) - 3) from x = 3.5 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0244 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2π(1|(-1(-5x^2 + 3x + 3) - 2) + 3|) - 3) - 3 and g(x) = -1cos(3π((-1(4x - 2) - 3)/(-3(4x - 2) + 2)) + 1) - 2 between the vertical lines x = 4.9 and x = 5.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0245 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-3cos(1π(3((-2x - 3)/(1x - 3))^2 + 5((-2x - 3)/(1x - 3)) - 3) - 1) + 1) + 3| - 3 and g(x) = 3|(3(-1sin(2πx) + 2)^2 + 5(-1sin(2πx) + 2) - 1) - 2| - 3 between the vertical lines x = 4.3 and x = 4.3999999999999995. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0246 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3(-2x - 5)^2 + 1(-2x - 5) - 1) - 3)/(-2(-3(-2x - 5)^2 + 1(-2x - 5) - 1) + 1) and g(x) = -3((-3x)/(-2x - 2))^2 - 3((-3x)/(-2x - 2)) + 4 between the vertical lines x = -0.5 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0247 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2|(1sin(1π(1x + 2) - 2) + 1) - 3| + 3 and g(x) = (-3(-1cos(1πx - 2)) + 2)/(3(-1cos(1πx - 2))) from x = -2.8 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 6.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0248 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-3((-2(2x^2 - 1x - 1) + 2)/(3(2x^2 - 1x - 1) - 1)) + 2) + 3| + 1 and g(x) = (-3(-3(-1x^2 - 4x - 3)) + 3)/(-2(-3(-1x^2 - 4x - 3))) between the vertical lines x = -3.0 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 31.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0249 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(5x^2 - 1)| + 1 and g(x) = 2x^2 + 1x - 3 between the vertical lines x = -0.9 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 4.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0250 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-1(1(-3cos(3πx - 3))^2 - 4(-3cos(3πx - 3)) + 2) - 1)/(1(1(-3cos(3πx - 3))^2 - 4(-3cos(3πx - 3)) + 2) - 3), g(x) = (1(-1x^2 + 3x + 1) + 2)/(-3(-1x^2 + 3x + 1) - 1), x = -1.2, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0251 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(3π(4((-3x - 3)/(3x - 2))) - 2) - 3 and g(x) = 3sin(3π(2x - 1) - 1) - 1 between the vertical lines x = -4.3 and x = -4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0252 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1(-4x^2 - 3x + 1) - 4, g(x) = 2x - 5, x = -1.6, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 4.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0253 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(1π(3|(-1x^2 + 3x - 3) - 1| - 3) - 3) + 1 and g(x) = 3|((1x + 1)/(-2x - 3)) - 3| - 2 between the vertical lines x = -1.4 and x = -1.2999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0254 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -5(3|(5((1x + 2)/(1x + 1))^2 + 4((1x + 2)/(1x + 1)) - 1) + 1| - 2) + 2 and g(x) = 1(2(-1|x - 2| + 1) + 4)^2 + 3(2(-1|x - 2| + 1) + 4) - 2 from x = -2.2 to x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 6.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0255 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-4(1x + 2)^2 + 4) + 3)/(2(-4(1x + 2)^2 + 4) + 2) and g(x) = 4((1x - 2)/(2x - 3)) + 5 between the vertical lines x = -0.9 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 38.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0256 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1(-2sin(1π((2(-1|x + 3| - 3) - 3)/(-3(-1|x + 3| - 3) - 2)) + 3) - 3)^2 - 1 and g(x) = -2((2(5x^2 - 5x + 5) + 1)/(3(5x^2 - 5x + 5) - 1)) + 5 from x = -4.0 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0257 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3(3|((-1(5x^2 - 4x) - 1)/(-2(5x^2 - 4x) + 1)) - 2|) - 4 and g(x) = -5(2((1x - 1)/(-2x + 1)) - 3)^2 - 4 from x = 0.8 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0258 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(3π((1(-4x^2 + 5x - 1) + 2)/(2(-4x^2 + 5x - 1) + 2)) + 3) and g(x) = -1sin(3π((2x - 1)/(2x + 3)) + 1) - 1 between the vertical lines x = 1.2 and 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_0259 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2sin(3π((1x + 1)/(2x - 1))), g(x) = (3x - 3)/(1x + 3), x = 0.6, and x = 0.7. 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_0260 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1|((-2x + 3)/(-1x + 3)) + 1| - 3, g(x) = (1x + 1)/(3x - 2), x = 0.3, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 20.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0261 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-1|(4x^2 - 5x + 4)| + 1))/(2(-1|(4x^2 - 5x + 4)| + 1) - 1) and g(x) = -3sin(1π((2x - 2)/(2x)) + 2) - 2 between the vertical lines x = 0.1 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0262 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1((1(2|(-2x^2 - 3x - 2)| - 2) - 1)/(-3(2|(-2x^2 - 3x - 2)| - 2) - 2)) + 2, g(x) = (-3(-2(1x + 3)^2 - 2(1x + 3) + 3) - 3)/(-2(-2(1x + 3)^2 - 2(1x + 3) + 3) + 1), x = -3.9, and x = -3.2. 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_0263 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((-2(-4x^2 - 5x + 2) + 2)/(-1(-4x^2 - 5x + 2) + 2)) + 3 and g(x) = -3|(-1x^2 - 2x - 1) - 3| - 3 between the vertical lines x = -1.0 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0264 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(5x^2 - 3) + 3)/(2(5x^2 - 3) - 3) and g(x) = -1|x + 1| + 1 from x = -2.5 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0265 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -5(-2x - 2)^2 + 3(-2x - 2) + 3, g(x) = -1x - 3, x = -1.6, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0266 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1(4(-1sin(1πx + 3) + 2) - 3)^2 - 3(4(-1sin(1πx + 3) + 2) - 3) + 4, g(x) = 3sin(1π(1x^2 + 1x - 2)) - 1, x = 1.7, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 45.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0267 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2|((2(1x^2 - 2x) - 2)/(2(1x^2 - 2x) - 3)) + 2| - 2) - 3 and g(x) = -3((-1(1|x| + 1) - 3)/(3(1|x| + 1) - 2)) + 1 between the vertical lines x = -0.6 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 10.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0268 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(5(3sin(3π((-3x)/(-2x - 2)))) - 4) + 3| - 3 and g(x) = 1|(-1e^(-2((-3x + 1)/(-2x - 1))) - 1) - 3| - 3 between the vertical lines x = -0.9 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0269 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4((1(-5(-2|x - 1| + 1) - 2) - 3)/(-1(-5(-2|x - 1| + 1) - 2) - 2))^2 - 1((1(-5(-2|x - 1| + 1) - 2) - 3)/(-1(-5(-2|x - 1| + 1) - 2) - 2)) and g(x) = -2cos(2π(-3|(2x^2 - 2x - 4) + 3| - 1) - 1) from x = -0.5 to 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_0270 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-1(2|x + 3| + 3)^2 + 2(2|x + 3| + 3) + 5) - 4 and g(x) = 2(1|x + 3| - 1) - 4 between the vertical lines x = -3.2 and x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0271 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((-2(3x + 2))/(-3(3x + 2) - 3)) - 3| and g(x) = -5(-1cos(3πx + 2) + 2) - 5 between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 5.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0272 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (2(1cos(1πx) - 2) - 3)/(-2(1cos(1πx) - 2) - 3), g(x) = 2|x + 2| - 2, x = 3.8, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0273 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3|((1(1(-2x + 4)^2 + 3(-2x + 4) - 1) - 1)/(-2(1(-2x + 4)^2 + 3(-2x + 4) - 1) + 3)) + 3| - 3, g(x) = 4((-2(-2|x - 1| + 1) + 1)/(3(-2|x - 1| + 1))) - 5, x = 0.3, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 41.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0274 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3((-1x)/(1x - 3))^2 - 5((-1x)/(1x - 3)) + 3, g(x) = 2|x| + 1, x = 0.5, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0275 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3cos(1π(-3(-1|x - 2| - 3) + 1) + 2) + 3, g(x) = -1(2|x + 1| - 1) + 5, x = 0.7, and x = 1.0. 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_0276 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(5x^2 - 5x - 3) - 2| - 2 and g(x) = -2|x + 3| + 3 between the vertical lines x = 1.4 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0277 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-1(3|x - 2| - 1) - 1)/(1(3|x - 2| - 1) - 3), g(x) = 2|x|, x = 1.1, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 6.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0278 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (2(5(-2cos(3πx - 1) - 1) - 5) + 1)/(-2(5(-2cos(3πx - 1) - 1) - 5) - 3), g(x) = 2(2cos(3πx + 3) - 3)^2 + 1(2cos(3πx + 3) - 3) - 5, x = -0.8, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 9.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0279 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(1cos(1πx - 1) + 1) + 3| - 1 and g(x) = 3|x| - 3 between the vertical lines x = -3.0 and x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0280 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((2(-1x + 2))/(-2(-1x + 2) + 1)) + 3| + 3 and g(x) = -1(-4x^2 - 2x - 5) + 1 between the vertical lines x = 1.5 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 10.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0281 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1|(1sin(3πx - 3) - 1) + 3| + 1, g(x) = 2x - 1, x = -0.3, and x = -0.0. 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_0282 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 3|(-3cos(2πx + 3)) + 1| - 1 and g(x) = (-1x - 2)/(-2x) from x = 0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0283 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1(1|(-2(-3cos(2πx + 2) - 3) - 2) - 3|)^2 - 5(1|(-2(-3cos(2πx + 2) - 3) - 2) - 3|) + 2 and g(x) = 1e^(1(-3(-5x + 3)^2 + 5(-5x + 3) + 4)) - 1 from x = -2.9 to x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0284 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3|(1cos(1πx - 3)) - 1| - 1 and g(x) = 5x + 3 from x = -2.0 to x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0285 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-2(3|(-2cos(2π(-1x^2 + 4x + 3) - 2) + 1) - 3| - 3) + 1)/(-2(3|(-2cos(2π(-1x^2 + 4x + 3) - 2) + 1) - 3| - 3)), g(x) = 2|(-1sin(1π(-5x^2 + 3x - 3) - 1)) - 3|, x = -0.2, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0286 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3|(1cos(3π((-1x + 1)/(-2x - 2)) - 3) + 2) + 1| and g(x) = -3|(1cos(2πx - 3) - 1) - 1| - 3 from x = -0.7 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0287 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π(-4x^2 + 5) - 2) + 1 and g(x) = -3x^2 + 4x + 3 between the vertical lines x = 1.1 and x = 1.2000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0288 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1|((-1x - 1)/(-3x + 2)) - 2| + 2 and g(x) = -4x - 4 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 23.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0289 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3|(-3((-3x + 1)/(1x + 1))^2 - 5((-3x + 1)/(1x + 1)) + 3) + 3|) + 2 and g(x) = (1(-5(1sin(3πx + 3) - 1)) + 1)/(-2(-5(1sin(3πx + 3) - 1)) - 3) between the vertical lines x = 0.0 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0290 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(3π((-3x + 3)/(-1x + 2)) - 3) + 3 and g(x) = (3x - 1)/(1x - 3) between the vertical lines x = -0.0 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0291 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(2π(1x^2 + 2x + 1)) + 3 and g(x) = 1x^2 + 2x - 2 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}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0292 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1|(-5x - 3) + 3| and g(x) = -1x - 2 from x = -0.3 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0293 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3x^2 + 4x + 1) - 2 and g(x) = (1x)/(-3x) between the vertical lines x = -0.3 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 16.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0294 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-1e^(-2x) + 2) - 1)/(2(-1e^(-2x) + 2) - 1) and g(x) = -2x^2 - 3x + 4 between the vertical lines x = -2.4 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 11.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0295 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-5(-3e^(1x) - 3)^2 - 3(-3e^(1x) - 3) - 2) + 1)/(2(-5(-3e^(1x) - 3)^2 - 3(-3e^(1x) - 3) - 2) - 1) and g(x) = -1|(-3sin(1πx - 2) + 1)| + 1 between the vertical lines x = -4.3 and x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0296 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1(-2|(1e^(1(-5x^2 + 3)) - 2) + 3| + 1) - 3 and g(x) = 1|(-3cos(1π(2x)) - 3) - 3| + 3 from x = -0.6 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 17.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0297 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-3(-5(4x - 3)^2 - 2(4x - 3) + 5) - 3)/(2(-5(4x - 3)^2 - 2(4x - 3) + 5) - 1), g(x) = 3|(-1x^2 - 5x + 3)| + 3, x = 0.4, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 7.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0298 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2|((-1(1x) + 1)/(-1(1x) - 1)) - 3| + 2, g(x) = 2sin(3π(-3x^2 - 1x - 2) - 1) + 1, x = -2.4, and x = -2.3. 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_0299 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(2((1x)/(3x))) and g(x) = -1|x| + 1 between the vertical lines x = -4.9 and x = 4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 24.0 | MATH_EXPLORATIVE |
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