id
string | setting_key
string | messages
list | ground_truth
string | dataset
string |
|---|---|---|---|---|
algebra_func_area_train_0300 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1(-2cos(2π(-3x^2 - 1x - 5) - 3) + 3) + 5 and g(x) = 2e^(-1(1x + 1)) + 3 from x = -2.1 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0301 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1cos(2πx))^2 - 4 and g(x) = -2x + 4 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_0302 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 5(-2cos(1πx - 2) - 3)^2 - 2(-2cos(1πx - 2) - 3) - 2, g(x) = 2|x - 2| + 1, x = -4.6, and x = -4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0303 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1e^(2((2(4(3x - 5)^2 + 4(3x - 5)) - 1)/(2(4(3x - 5)^2 + 4(3x - 5)) - 1))) + 1 and g(x) = -1(-3sin(2π((1x - 3)/(2x - 3)) + 1))^2 + 2(-3sin(2π((1x - 3)/(2x - 3)) + 1)) + 3 from x = 1.7 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0304 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 1(2e^(1x) + 2)^2 + 2, g(x) = -1x^2 - 5x + 4, x = -4.5, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 8.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0305 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(3|(-4((-2x - 2)/(-1x + 2))^2 - 4((-2x - 2)/(-1x + 2)) + 3) + 3|) + 5 and g(x) = 1cos(1π(-3(-2|x| - 1) - 3) + 3) - 1 between the vertical lines x = -3.3 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0306 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1((-1(-5(3|x - 3| - 3) - 1) + 3)/(1(-5(3|x - 3| - 3) - 1) - 2))^2 - 2((-1(-5(3|x - 3| - 3) - 1) + 3)/(1(-5(3|x - 3| - 3) - 1) - 2)) - 3, g(x) = -2(4((-2x - 1)/(3x + 3))^2 + 5((-2x - 1)/(3x + 3)) + 3) - 5, x = 2.2, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 8.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0307 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 5(-1|(-1e^(1(1x^2 + 1x - 4)) + 2) + 2|) + 4 and g(x) = (2(-1(-5x - 2)^2 - 1(-5x - 2) + 5) + 1)/(-1(-1(-5x - 2)^2 - 1(-5x - 2) + 5) + 3) from x = 1.8 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0308 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2|((1(-5x - 5) - 2)/(-3(-5x - 5) + 4))| - 3, g(x) = (-1(-2|x - 2|) + 1)/(-3(-2|x - 2|) - 1), x = -1.2, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 10.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0309 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-1(1(-1|(-4x) + 2| - 2)^2 + 3(-1|(-4x) + 2| - 2) - 3) - 3)/(-3(1(-1|(-4x) + 2| - 2)^2 + 3(-1|(-4x) + 2| - 2) - 3) + 2) and g(x) = 4(-2|((1x + 1)/(-1x + 2)) - 2| + 3) - 1 from x = 1.0 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0310 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2|(3cos(3π(2x + 1) - 3) - 2) + 2| - 1 and g(x) = 1sin(3π(5x + 2) + 1) + 2 from x = 4.1 to x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0311 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-3(-1((3x + 3)/(-1x + 3))^2 - 5((3x + 3)/(-1x + 3)) - 5) + 1) + 2| - 3 and g(x) = (2(-2cos(1π(-5x^2 + 5x + 5) - 3) - 1) + 3)/(2(-2cos(1π(-5x^2 + 5x + 5) - 3) - 1) - 1) between the vertical lines x = -3.0 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0312 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4((3(-2sin(3πx - 2)))/(-1(-2sin(3πx - 2)) - 1))^2 - 4((3(-2sin(3πx - 2)))/(-1(-2sin(3πx - 2)) - 1)) and g(x) = 1(3cos(1πx + 1) + 2)^2 + 2(3cos(1πx + 1) + 2) - 4 from x = -1.4 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0313 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2cos(1π(1|x + 3|) - 3) + 1 and g(x) = 1|x + 1| - 1 from x = 0.4 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0314 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3(1((-1x - 1)/(1x + 1))^2 - 2) - 3, g(x) = -3(-4x^2 + 5x + 2) - 3, x = -0.4, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 19.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0315 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1((-2(-3(2|x - 3| + 1)^2 + 1(2|x - 3| + 1) + 3) - 3)/(2(-3(2|x - 3| + 1)^2 + 1(2|x - 3| + 1) + 3) - 1)) and g(x) = 5(1|(1sin(1πx + 2)) + 1| - 3)^2 + 2(1|(1sin(1πx + 2)) + 1| - 3) - 1 from x = 3.0 to x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 7.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0316 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3cos(1π((2x + 1)/(-2x - 2)) - 3) + 3) + 5 and g(x) = (2(-3|x + 1| - 2) + 3)/(1(-3|x + 1| - 2) + 2) 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}"
}
]
| 0.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0317 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-1|x| + 2) - 3)/(-2(-1|x| + 2)) and g(x) = -5x - 1 between the vertical lines x = -1.8 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 4.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0318 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1(3|(5((-2x)/(-2x - 2))^2 + 2((-2x)/(-2x - 2)) + 1) - 3| + 3) + 4 and g(x) = -2e^(-1((-3(3x^2 - 4x + 1) - 2)/(1(3x^2 - 4x + 1) + 3))) + 3 from x = -0.6 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0319 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1cos(1π((3x + 1)/(-2x)) - 2) + 3, g(x) = -2x^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}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0320 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2cos(3π(-4(-1x^2 + 3x - 2) - 2) + 2) - 2, g(x) = (1(4x - 1) + 2)/(2(4x - 1)), x = -0.2, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0321 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2(5(3|(-1cos(1πx) - 2)| - 3) - 5)^2 + 5, g(x) = -3(-1|(-4x^2 + 4x - 3) + 2| - 3) - 5, x = 0.7, and x = 0.7999999999999999. 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_0322 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2|(1cos(3π(5(3x + 1)^2 + 5(3x + 1) + 5) + 1) + 3) + 1| - 1, g(x) = 1(2cos(2π(-2x - 4) - 3) - 3)^2 - 1(2cos(2π(-2x - 4) - 3) - 3) + 2, x = 4.8, and x = 4.8999999999999995. 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_0323 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2|(4(1cos(2πx - 3) - 2)^2 + 4(1cos(2πx - 3) - 2) + 3) - 2| and g(x) = -3|(1x) - 2| + 2 from x = 3.5 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 18.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0324 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2|(-5(3sin(2π(2x^2 - 5x - 5)) + 2) + 3) + 2| - 1 and g(x) = (-3(5(-3|x| - 2)^2 + 3(-3|x| - 2) - 3) - 2)/(1(5(-3|x| - 2)^2 + 3(-3|x| - 2) - 3)) from x = -3.0 to x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0325 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(-1(3cos(3π(-3|x - 3| - 2) - 3) - 2) + 4)^2 + 5(-1(3cos(3π(-3|x - 3| - 2) - 3) - 2) + 4) - 5 and g(x) = -2(-2|((-2x + 3)/(-2x)) + 3| - 3)^2 + 3(-2|((-2x + 3)/(-2x)) + 3| - 3) + 1 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0326 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((1(5(-2cos(3πx + 3) - 1)) + 1)/(1(5(-2cos(3πx + 3) - 1)))) + 2| - 3 and g(x) = -1sin(2π((3(-3x^2 + 4x - 4))/(2(-3x^2 + 4x - 4) + 1)) - 2) + 1 between the vertical lines x = -0.8 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0327 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-3(-3sin(1π(2(2x + 1)^2 + 4(2x + 1) + 2) + 2) - 1) + 2)/(1(-3sin(1π(2(2x + 1)^2 + 4(2x + 1) + 2) + 2) - 1) + 3), g(x) = 1(2|(-5x^2 - 2x + 5) + 3| + 2) + 2, x = 0.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 5.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0328 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 5(1sin(2π((2(-2|x + 2|) - 2)/(1(-2|x + 2|))) - 2) - 2) - 2 and g(x) = -4((-3(-5x + 3))/(1(-5x + 3) - 3))^2 - 4 from x = 0.4 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0329 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3((2(-5x^2 + 2x + 4) - 3)/(1(-5x^2 + 2x + 4) - 2)) + 2, g(x) = (-1(2|x + 3| - 2) + 2)/(2(2|x + 3| - 2) - 3), x = -1.2, and x = -0.5. 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_0330 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -5(-2|(-3x + 2) - 2| - 3)^2 + 2(-2|(-3x + 2) - 2| - 3) + 4, g(x) = -2((-3x - 3)/(2x))^2 + 1, x = -0.2, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| -68.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0331 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2cos(3π(3(-2|x - 3| - 3)^2 - 2(-2|x - 3| - 3) - 4) + 3) + 1 and g(x) = (1(2|x + 2|) - 3)/(-2(2|x + 2|)) from x = 1.1 to 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_0332 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(2e^(-2(5(-5x + 2)^2 - 5(-5x + 2) + 4)) - 1) - 1| - 1 and g(x) = -3(1((-3x + 2)/(-2x + 1))^2 - 4((-3x + 2)/(-2x + 1)) - 5) - 2 between the vertical lines x = 0.4 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| -46.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0333 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2sin(2π(-1x - 2) - 2) + 1, g(x) = -2|x + 1| + 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}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0334 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-2sin(2πx) - 1) - 3| + 3 and g(x) = -1x + 3 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}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0335 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1|(-3(-5x^2 - 5x + 2)) - 3| - 1, g(x) = -3|(4x - 2) + 2| - 1, x = 0.3, and x = 0.7. 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_0336 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-5(1(-2|x + 1| - 1)^2 + 4(-2|x + 1| - 1) + 2) + 3) + 3)/(-1(-5(1(-2|x + 1| - 1)^2 + 4(-2|x + 1| - 1) + 2) + 3) + 3) and g(x) = (3(-4(-2x^2 - 3x + 1)) + 1)/(-3(-4(-2x^2 - 3x + 1)) - 1) between the vertical lines x = -2.4 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 18.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0337 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-2(-1|(-3sin(2π(2x^2 + 3x - 4) - 1) + 2) + 1| - 3))/(3(-1|(-3sin(2π(2x^2 + 3x - 4) - 1) + 2) + 1| - 3) - 2), g(x) = -4((2(-1x + 2) + 1)/(1(-1x + 2) - 2))^2 + 2, x = 1.8, and x = 4.2. 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_0338 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2|(-2e^(-1x) + 3) - 2| - 3 and g(x) = (-1x - 3)/(-1x + 2) from x = 0.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0339 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2(-1|x + 2| + 1) - 2, g(x) = 5x^2 + 1x - 5, x = -0.9, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 6.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0340 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 3|(2(-1x + 3)^2 - 5) - 3|, g(x) = (-3(-1|x - 3| - 1) - 1)/(1(-1|x - 3| - 1) + 2), x = 2.2, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 25.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0341 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3|(-3cos(2π(5x + 5) - 1) + 1) + 1| + 3)^2 + 2 and g(x) = (2(3|(3cos(2πx + 3) - 2) + 1| - 3) - 1)/(3(3|(3cos(2πx + 3) - 2) + 1| - 3) - 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}"
}
]
| 3.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0342 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((1(4x - 1) + 1)/(-2(4x - 1) - 2))^2 - 5((1(4x - 1) + 1)/(-2(4x - 1) - 2)) - 1 and g(x) = (-2(2|x + 1| - 2) + 3)/(3(2|x + 1| - 2) - 2) between the vertical lines x = -2.5 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 23.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0343 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(1((2x + 1)/(1x + 1)))^2 - 5(1((2x + 1)/(1x + 1))) - 3 and g(x) = 3cos(2π(2|x + 2|) + 1) + 1 between the vertical lines x = 3.0 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0344 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-2cos(2π(1|x + 2| - 2) - 1) + 1) - 3)/(3(-2cos(2π(1|x + 2| - 2) - 1) + 1) - 2) and g(x) = (1(-3cos(3πx + 2) + 3))/(3(-3cos(3πx + 2) + 3) + 1) between the vertical lines x = -2.2 and 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_0345 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -3(-2((1(-1cos(1πx) + 1) + 3)/(-2(-1cos(1πx) + 1) - 1)) - 2)^2 + 1(-2((1(-1cos(1πx) + 1) + 3)/(-2(-1cos(1πx) + 1) - 1)) - 2) + 3, g(x) = 3|(3cos(1π((-2x - 1)/(2x - 3)) + 1) + 1) - 1| - 2, x = 1.3, and x = 1.4000000000000001. 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_0346 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((3x + 2)/(-2x))^2 - 2 and g(x) = 5x + 3 between the vertical lines x = -0.3 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| -6.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0347 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-4x^2 - 4x + 3) + 3)/(-1(-4x^2 - 4x + 3)) and g(x) = 2x^2 + 5x - 1 between the vertical lines x = -1.4 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0348 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(1(1(-3sin(1πx - 2) + 2)^2 + 5(-3sin(1πx - 2) + 2) + 1) - 2) - 2)/(3(1(1(-3sin(1πx - 2) + 2)^2 + 5(-3sin(1πx - 2) + 2) + 1) - 2) - 1) and g(x) = -3|(3(2x^2 - 2x - 2) + 4) + 3| from x = -0.6 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 8.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0349 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4(-3((1x - 2)/(-2x - 2))^2 + 2((1x - 2)/(-2x - 2)) - 1) - 4 and g(x) = 2sin(3π((-2x + 3)/(-2x + 3))) + 2 from x = 0.1 to x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 6.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0350 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1|(2cos(3π(3x^2 - 5x + 2) + 2) - 1) + 3| - 1, g(x) = -5(3x - 5)^2 - 2(3x - 5) + 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}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0351 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2e^(1(3x - 4)) + 3))/(1(2e^(1(3x - 4)) + 3) - 2) and g(x) = 2|(4x - 3)| + 2 between the vertical lines x = 0.7 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0352 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-3x + 5) + 3)/(2(-3x + 5) + 1) and g(x) = 3x + 1 between the vertical lines x = -0.7 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 7.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0353 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1(3x^2 - 2x + 3) - 1, g(x) = -2|x + 1| - 3, x = -0.2, and x = 1.6. 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_0354 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-5(5x + 2)^2 + 2(5x + 2) - 4))/(3(-5(5x + 2)^2 + 2(5x + 2) - 4) + 2) and g(x) = 2|((1x - 2)/(1x + 1)) + 1| - 2 between the vertical lines x = 0.1 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0355 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -2(3sin(3π(-2((1x)/(-1x + 2))^2 + 2) - 2) - 1) and g(x) = -2|(-1(2x + 4)^2 - 5(2x + 4)) - 1| from x = -4.6 to x = -4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.8 | MATH_EXPLORATIVE |
algebra_func_area_train_0356 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (3(-2cos(1π(2|(2x^2 - 3) + 2| + 2)) - 3) - 3)/(2(-2cos(1π(2|(2x^2 - 3) + 2| + 2)) - 3) - 1), g(x) = (-3(2|(-4x + 5) + 1| - 3) + 1)/(2(2|(-4x + 5) + 1| - 3) + 1), x = 1.1, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 10.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0357 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -1sin(2π(4((-1(3|x| + 1) - 1)/(1(3|x| + 1) - 2)) - 3) + 1) - 3 and g(x) = 3((1(-2e^(1x) - 1) + 2)/(-1(-2e^(1x) - 1) + 2)) - 1 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0358 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(1π((2(-5x^2 + 3x) + 1)/(1(-5x^2 + 3x) + 1)) + 3) + 1 and g(x) = -1|(-2sin(1πx + 1) - 1)| + 2 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}"
}
]
| 0.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0359 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -3e^(1(5((-3x)/(3x + 2)) + 5)) - 3 and g(x) = (2(2sin(1πx + 1)) + 3)/(1(2sin(1πx + 1)) + 1) from x = -2.5 to x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 15.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0360 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-4(-2|x + 1| + 2)^2 + 2(-2|x + 1| + 2) + 2) - 1)/(-1(-4(-2|x + 1| + 2)^2 + 2(-2|x + 1| + 2) + 2) + 2) and g(x) = -3e^(-1(1x + 3)) + 3 between the vertical lines x = -3.7 and x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 3.5 | MATH_EXPLORATIVE |
algebra_func_area_train_0361 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(-1(3|(-2cos(1πx + 3) + 3) - 2| - 3) - 1) - 2)/(-3(-1(3|(-2cos(1πx + 3) + 3) - 2| - 3) - 1) - 1) and g(x) = (1(1(2sin(2πx + 3) - 3)^2 - 1(2sin(2πx + 3) - 3) + 5) - 3)/(2(1(2sin(2πx + 3) - 3)^2 - 1(2sin(2πx + 3) - 3) + 5) + 2) from x = 2.6 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0362 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (-3(3sin(2π(-2x^2 - 5x - 5))) + 1)/(-2(3sin(2π(-2x^2 - 5x - 5))) + 3) and g(x) = 1sin(1π(5x^2 - 3x + 1) - 1) + 1 from x = -3.7 to 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_0363 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(2e^(2((3x - 3)/(-2x - 2))) + 2) - 2| - 2 and g(x) = 2(-3cos(2πx - 3) + 2) - 2 between the vertical lines x = 2.4 and 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_0364 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4(3((2(-2e^(1x) + 3) + 1)/(1(-2e^(1x) + 3) - 2))^2 - 2((2(-2e^(1x) + 3) + 1)/(1(-2e^(1x) + 3) - 2))) + 4 and g(x) = 1(2|(-2x^2 + 1x - 3) + 2| - 1) + 3 from x = 0.6 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_0365 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (3(1|x + 1| - 1) + 3)/(1(1|x + 1| - 1) + 3) and g(x) = 1x^2 + 2x + 1 from x = -2.0 to 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_0366 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2|(5(5x^2 - 5x + 4) - 4) + 2| + 2, g(x) = 3(2sin(1πx + 2) - 2)^2 - 5(2sin(1πx + 2) - 2) - 4, x = 0.4, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 14.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0367 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2e^(-1(-1|(5(-3x - 3)^2 + 5(-3x - 3) - 1)| + 3)) - 2 and g(x) = -1((2(2|x + 2| - 3) + 3)/(-3(2|x + 2| - 3) - 1))^2 - 5((2(2|x + 2| - 3) + 3)/(-3(2|x + 2| - 3) - 1)) - 2 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}"
}
]
| 0.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0368 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 2(2cos(3π((-2x + 3)/(-1x + 2)) + 3) - 3) + 2 and g(x) = -5((1x - 1)/(3x + 2))^2 - 3((1x - 1)/(3x + 2)) - 1 from x = 1.6 to x = 1.7000000000000002. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0369 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = (2(-2x^2 - 5x + 1) - 1)/(1(-2x^2 - 5x + 1) + 2) and g(x) = -3x - 3 from x = -3.2 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 38.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0370 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3cos(2π(-3|x| + 3) + 1) - 3 and g(x) = -3x + 4 between the vertical lines x = 1.8 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0371 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3(1|(4x^2 - 3x - 1)| - 1) - 3) + 3)/(1(-3(1|(4x^2 - 3x - 1)| - 1) - 3) + 1) and g(x) = (1(1(1|x + 3| - 3) + 2) + 3)/(2(1(1|x + 3| - 3) + 2) + 3) between the vertical lines x = -1.9 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0372 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(1(-4(3|x + 1| - 1)^2 + 4(3|x + 1| - 1) + 2) - 4) - 2)/(-3(1(-4(3|x + 1| - 1)^2 + 4(3|x + 1| - 1) + 2) - 4) - 2) and g(x) = 4(3cos(3π(-2|x + 2|) + 2) - 1) + 2 between the vertical lines x = 4.0 and x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0373 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2((1(-3|x + 3|) + 2)/(-2(-3|x + 3|) + 1))^2 - 3((1(-3|x + 3|) + 2)/(-2(-3|x + 3|) + 1)) + 5, g(x) = 3|(-1e^(1x) + 2) - 2| + 1, x = -3.2, and x = -2.8. 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_0374 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (1(-2(-3|(2x^2 - 5x - 1) + 2|) - 2) + 3)/(2(-2(-3|(2x^2 - 5x - 1) + 2|) - 2) + 3), g(x) = -1(-1|(-1x - 2) + 1| - 1)^2 - 5(-1|(-1x - 2) + 1| - 1) + 2, x = 0.2, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 14.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0375 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2cos(2π(-2|(-1(4x^2 + 1x - 5) + 1) - 2| + 3) - 2) - 2, g(x) = -4((2(-2|x| + 3) - 2)/(1(-2|x| + 3) + 3)) + 1, x = 0.4, and x = 0.5. 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_0376 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(4(-3|(-3x - 5) + 3|)^2 + 3(-3|(-3x - 5) + 3|)) - 2)/(3(4(-3|(-3x - 5) + 3|)^2 + 3(-3|(-3x - 5) + 3|))) and g(x) = 3|(-1((2x + 1)/(-2x - 1)) + 2) - 1| - 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}"
}
]
| 1.3 | MATH_EXPLORATIVE |
algebra_func_area_train_0377 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 2(1|(-1x) - 3|)^2 - 4(1|(-1x) - 3|) + 2, g(x) = -5(-2cos(2πx - 3) + 2) + 3, x = -2.4, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 7.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0378 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -4(2((2(2|x + 3|) + 1)/(1(2|x + 3|) + 1))^2 - 4((2(2|x + 3|) + 1)/(1(2|x + 3|) + 1)) - 1) - 3, g(x) = 5((1(-2x^2 - 3) + 1)/(2(-2x^2 - 3) - 3)) + 2, x = -4.6, and x = 0.0. 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_0379 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 5((1(3(3|x - 1| - 2) - 5) - 3)/(-1(3(3|x - 1| - 2) - 5) - 1))^2 + 5((1(3(3|x - 1| - 2) - 5) - 3)/(-1(3(3|x - 1| - 2) - 5) - 1)), g(x) = (-3(-4(-2|x - 2| - 2)^2 - 1(-2|x - 2| - 2) - 1) - 2)/(3(-4(-2|x - 2| - 2)^2 - 1(-2|x - 2| - 2) - 1) - 1), x = 2.7, and x = 3.7. 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_0380 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (3(-2cos(1π(4x^2 - 2x - 4) + 3) + 2) - 1)/(-2(-2cos(1π(4x^2 - 2x - 4) + 3) + 2) + 3), g(x) = 1(1sin(3πx - 1) + 2)^2 + 5(1sin(3πx - 1) + 2) + 5, x = -4.0, and x = -3.9. 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_0381 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1cos(2π(-2x^2 - 1x + 4) - 2) - 1, g(x) = -5x^2 + 5x + 2, x = 1.4, and x = 1.5. 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_0382 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-4(2cos(2π(-5x^2 - 2x - 4) - 1) - 3) - 3) + 1| - 3 and g(x) = (1(3(-1|x + 3| + 3)^2 - 5(-1|x + 3| + 3) - 5) + 1)/(-3(3(-1|x + 3| + 3)^2 - 5(-1|x + 3| + 3) - 5)) 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}"
}
]
| 0.7 | MATH_EXPLORATIVE |
algebra_func_area_train_0383 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3cos(1π(1((-2x)/(-1x - 2)) + 4) + 1) + 3)^2 - 4(-3cos(1π(1((-2x)/(-1x - 2)) + 4) + 1) + 3) + 1 and g(x) = -2|((-1(1x) - 1)/(1(1x) - 2))| - 1 between the vertical lines x = 2.2 and x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 14.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0384 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(2π((-2(-3|x - 2| - 3) + 3)/(1(-3|x - 2| - 3))) - 3) + 1 and g(x) = 4(2sin(1πx + 3) + 1) - 1 between the vertical lines x = -1.9 and 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_0385 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (-2(-1|(2x^2 + 5x) + 2| - 2) - 1)/(3(-1|(2x^2 + 5x) + 2| - 2) - 2), g(x) = 2(3|x - 2| - 3) - 2, x = 0.8, and x = 3.2. 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_0386 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2(-4(-2|((1x - 1)/(-3x)) - 1| + 1)^2 - 2(-2|((1x - 1)/(-3x)) - 1| + 1) + 3) - 5, g(x) = -2(-2|(1sin(2πx - 3) - 3) + 3|)^2 + 3(-2|(1sin(2πx - 3) - 3) + 3|) + 5, x = 1.6, and x = 1.9. 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_0387 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3cos(2πx - 1) + 2) - 2)/(2(-3cos(2πx - 1) + 2) + 3) and g(x) = 2|x + 2| - 2 between the vertical lines x = -1.8 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0388 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = (3(1(2e^(-2x)) - 2) + 1)/(-3(1(2e^(-2x)) - 2) - 3), g(x) = 2|((3x + 3)/(-2x + 1)) - 3| - 2, x = 0.1, and x = 0.3. 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_0389 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-1x^2 - 2x - 2) - 2)/(-2(-1x^2 - 2x - 2) - 3) and g(x) = -1x + 4 between the vertical lines x = -0.3 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 9.4 | MATH_EXPLORATIVE |
algebra_func_area_train_0390 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-1(1x + 1)^2 - 4(1x + 1) - 5) - 2)/(-2(-1(1x + 1)^2 - 4(1x + 1) - 5)) and g(x) = -2sin(1π(-1|x + 3|) - 3) - 1 between the vertical lines x = -0.9 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 1.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0391 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -1e^(-1(-4(1|((-1x + 2)/(-2x - 1)) + 1| - 2) + 1)), g(x) = 1cos(1π(2(-1x - 5)^2 + 2(-1x - 5) + 1) - 2) - 1, x = -2.0, and x = -1.9. 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_0392 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = -4(2cos(1π(-2|x - 3| + 1) - 2) + 2) + 3 and g(x) = 5(-2|x + 2| + 3)^2 - 4(-2|x + 2| + 3) - 2 from x = -3.8 to x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.6 | MATH_EXPLORATIVE |
algebra_func_area_train_0393 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((2x + 1)/(3x + 2)) - 4 and g(x) = (3x - 3)/(1x + 2) between the vertical lines x = -0.9 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 5.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0394 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = 5((2(-1x + 2) - 1)/(3(-1x + 2) + 2))^2 + 4((2(-1x + 2) - 1)/(3(-1x + 2) + 2)) - 5, g(x) = (-2(-1x - 4) + 2)/(2(-1x - 4) + 3), x = -0.6, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 6.0 | MATH_EXPLORATIVE |
algebra_func_area_train_0395 | algebra_func_area | [
{
"role": "user",
"content": "Calculate the area enclosed between the functions f(x) = 1e^(-1((-2x)/(3x + 2))) and g(x) = 3x^2 - 1x + 1 from x = -0.0 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0396 | algebra_func_area | [
{
"role": "user",
"content": "Find the area of the region bounded by the curves f(x) = -2(-2(1|((2x)/(-3x + 1)) + 1|) + 5)^2 - 3(-2(1|((2x)/(-3x + 1)) + 1|) + 5) - 5, g(x) = -2|(-1e^(1(3x^2 - 4x + 3)) + 1) - 2| + 2, x = 0.4, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.9 | MATH_EXPLORATIVE |
algebra_func_area_train_0397 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-5(-3e^(-2x) + 3)^2 + 4(-3e^(-2x) + 3) - 4) + 2| and g(x) = 5(2|x + 3| - 3) - 5 between the vertical lines x = -0.1 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 2.2 | MATH_EXPLORATIVE |
algebra_func_area_train_0398 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(3(3|(1cos(1πx - 2) + 1) + 2| - 3)) - 3)/(2(3(3|(1cos(1πx - 2) + 1) + 2| - 3)) + 1) and g(x) = (1(3(-4x^2 + 3x + 1) - 2))/(1(3(-4x^2 + 3x + 1) - 2) + 2) between the vertical lines x = 0.0 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.1 | MATH_EXPLORATIVE |
algebra_func_area_train_0399 | algebra_func_area | [
{
"role": "user",
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-2|x - 3|)^2 - 4(-2|x - 3|) + 4 and g(x) = 3|x - 3| + 3 between the vertical lines x = 2.6 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
]
| 0.9 | MATH_EXPLORATIVE |
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