messages listlengths 1 1 | ground_truth stringlengths 3 5 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3sin(1π(-2x^2 - 5x + 1) - 1), g(x) = 5x^2 - 2x - 2, x = -0.3, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(1x^2 - 2x + 1)^2 - 5(1x^2 - 2x + 1) + 4 and g(x) = (2x - 1)/(-2x + 1) from x = -0.9 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(-2x + 3) + 1, g(x) = 3x^2 + 1x + 3, x = -3.1, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(1x^2 - 1x - 1))/(-1(1x^2 - 1x - 1) + 2), g(x) = 3x^2 - 3x + 2, x = -1.4, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1sin(2π(1x + 1) - 3) - 2, g(x) = 1|x - 2| - 2, x = 1.4, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4(5x^2 - 3x - 4)^2 - 4(5x^2 - 3x - 4) + 2 and g(x) = (-3x + 1)/(2x) from x = -0.4 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(3|x + 2| - 1)^2 + 5(3|x + 2| - 1) - 3 and g(x) = -3x - 3 from x = -2.6 to x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3((2x + 3)/(1x + 2))^2 - 4((2x + 3)/(1x + 2)) - 3 and g(x) = -5x^2 + 4x - 1 from x = -2.8 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2π(1|x| + 1) - 1) + 1 and g(x) = -2|x - 1| + 1 between the vertical lines x = 1.1 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2cos(1π(-2x + 4) - 1) - 1 and g(x) = -5x^2 + 5x - 2 from x = 0.1 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2sin(1π((-1x + 3)/(-1x + 2)) + 2) - 2 and g(x) = -2|x - 2| from x = 2.1 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1((2x - 3)/(3x + 1)) + 4 and g(x) = (1x + 1)/(-3x - 2) from x = -0.8 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5(3sin(1πx - 1)) + 3 and g(x) = (1x + 1)/(-1x + 2) from x = -3.8 to x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|((-1x)/(-3x)) + 1|, g(x) = -2x^2 + 3x - 1, x = -0.4, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(-2x - 4) + 3 and g(x) = (3x)/(1x - 2) from x = -1.6 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-3sin(3πx + 3) + 1) + 3| - 1 and g(x) = -5x^2 - 4x + 3 between the vertical lines x = -0.2 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(5x^2 - 4x - 1) - 3, g(x) = -4x - 5, x = -0.2, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|((-3x - 2)/(-3x)) + 3| - 3, g(x) = -5x^2 - 4x + 1, x = -0.4, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-1cos(2πx + 3) - 1) + 1)/(-2(-1cos(2πx + 3) - 1) + 1) and g(x) = 1x^2 - 4x from x = -0.1 to x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(-1e^(1x) + 2) - 3)/(-3(-1e^(1x) + 2) - 2), g(x) = (1x + 3)/(2x + 3), x = -2.7, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3((3x - 1)/(-3x - 1))^2 - 5((3x - 1)/(-3x - 1)) - 5 and g(x) = -4x^2 - 1x - 5 from x = -0.1 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(3e^(1x) - 2)^2 + 5(3e^(1x) - 2) - 3, g(x) = -5x - 4, x = -0.3, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2|x + 3| - 2) + 3)/(2(-2|x + 3| - 2) + 3) and g(x) = 1|x + 2| 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}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3|x - 1|)^2 + 4(-3|x - 1|) + 2 and g(x) = -3x^2 + 3x - 1 between the vertical lines x = 0.8 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2e^(-2(-2x + 2)) + 2 and g(x) = 1|x + 3| - 1 from x = 0.0 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(4x) + 3)/(-1(4x) - 1) and g(x) = (-3x + 2)/(1x + 2) between the vertical lines x = -0.4 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1((-3x - 2)/(1x - 3)) - 1, g(x) = 1|x + 1| - 1, x = -1.6, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(-4x^2 + 3x + 5) + 4 and g(x) = -1|x + 1| - 1 from x = -1.3 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2sin(3π(-1x - 1)) - 1, g(x) = 5x, x = -0.4, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1cos(2π(2|x + 1| - 3) - 2), g(x) = 2x - 2, x = 1.3, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-3x^2 + 3x + 1) + 4 and g(x) = (1x - 3)/(-3x - 3) between the vertical lines x = -0.9 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(2sin(2πx - 3) + 1) - 1)/(-1(2sin(2πx - 3) + 1) + 2) and g(x) = 1x^2 - 5x + 5 from x = -3.4 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(-3cos(3πx + 2) - 1) - 4, g(x) = 2|x + 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}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3e^(2(2x^2 + 1x - 4)) + 2, g(x) = 2x^2 + 3x + 2, x = 0.0, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2sin(1π(2|x + 2|)) + 1, g(x) = -2|x - 2| + 2, x = 0.9, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(2π((1x + 3)/(3x + 2)) - 1) - 3 and g(x) = (-1x + 3)/(3x - 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}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3cos(2π(-3|x + 1| - 2) - 2) + 2, g(x) = (1x - 2)/(-1x + 2), x = -4.4, and x = -4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2((2x + 3)/(3x + 3)) - 3 and g(x) = (-2x + 2)/(-1x + 2) from x = -0.8 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3sin(3π((1x - 3)/(1x)) + 1) - 2, g(x) = 5x^2 + 5x - 2, x = -0.2, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-1cos(3πx + 3) + 3) - 3)/(2(-1cos(3πx + 3) + 3) - 3), g(x) = -3x^2 - 5x + 2, x = 1.0, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(1sin(3πx - 1)) + 2)/(2(1sin(3πx - 1)) - 1), g(x) = (3x - 3)/(-1x - 2), x = -3.8, and x = -3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(1x - 2)^2 + 2(1x - 2) + 4, g(x) = (-3x)/(-2x - 2), x = 1.3, and x = 3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(2π(-1x - 3)) and g(x) = -1x^2 - 1x + 4 between the vertical lines x = -1.8 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2cos(3π(-5x + 2) - 3), g(x) = 2x^2 - 4x + 2, x = 1.0, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2e^(1(1x - 2)) - 2, g(x) = -3|x| + 2, x = 2.0, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(1(1x - 1)) - 1 and g(x) = (-3x - 1)/(-1x) between the vertical lines x = -0.3 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2sin(1π(-1x - 4)) - 2 and g(x) = 3x^2 + 5x - 5 from x = -2.3 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|((2x)/(-1x + 2)) - 3| - 1 and g(x) = -1x - 2 from x = 1.0 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2sin(2π((-3x - 3)/(-1x + 2)) - 1) - 1 and g(x) = (-2x + 1)/(2x - 3) from x = 2.3 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(1π(-1|x + 3|)) - 1 and g(x) = (-1x - 3)/(1x + 2) between the vertical lines x = -4.2 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 21.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2cos(3π((-3x - 3)/(1x + 3))) - 2, g(x) = -1x^2 + 5x, x = -0.1, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(1x^2 - 5), g(x) = -1x + 2, x = -1.3, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(3|x| - 1) - 3| + 2 and g(x) = 2|x| - 2 between the vertical lines x = 1.0 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1sin(2π(-1|x| + 3) - 3) + 1 and g(x) = -4x^2 - 5x + 1 from x = -0.1 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1((3x + 3)/(-1x + 3)) - 1)/(2((3x + 3)/(-1x + 3)) - 1) and g(x) = -5x - 3 from x = -0.8 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(5x^2 + 5x - 1)| + 2 and g(x) = -3|x + 3| + 3 from x = -1.6 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(1e^(1x) + 1) - 2| + 2 and g(x) = -4x^2 + 3 from x = -0.4 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2e^(-1(-2|x + 1|)) - 1, g(x) = (-3x - 1)/(-1x), x = -0.8, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4(5x) + 3 and g(x) = (3x - 2)/(-3x - 2) from x = -0.6 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(-3cos(1πx + 3) - 2))/(-1(-3cos(1πx + 3) - 2) - 1), g(x) = -3x + 2, x = 1.7, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(2|x - 3| - 3) - 2)/(3(2|x - 3| - 3) + 2), g(x) = -2x - 1, x = -0.1, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3e^(-2(2x^2 - 4x - 1)) - 1 and g(x) = -4x - 4 between the vertical lines x = -0.8 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3sin(1πx - 2) + 3)^2 + 4(-3sin(1πx - 2) + 3) and g(x) = -3x^2 + 3x + 4 between the vertical lines x = -1.7 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 5.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2sin(1π(3x - 2) - 1) - 2 and g(x) = -4x^2 - 2x + 3 from x = -1.5 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2cos(1π(-3x) + 1) - 2 and g(x) = -3|x - 3| - 1 from x = 2.3 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1e^(-2(2x^2 - 1)) - 3 and g(x) = 2x^2 - 4x + 1 from x = -0.3 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-3|x - 2|)^2 - 4(-3|x - 2|) + 1, g(x) = 1|x - 2| + 2, x = 1.9, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(-2x + 1)^2 - 1(-2x + 1) + 4 and g(x) = 3|x - 3| + 3 from x = -0.8 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|(2x^2 + 3x - 1) - 3|, g(x) = -4x^2 - 1x + 2, x = 0.8, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1π(-5x - 4)) + 1 and g(x) = -3x - 1 between the vertical lines x = -0.4 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(3sin(2πx - 2) - 1)^2 + 2(3sin(2πx - 2) - 1) + 2, g(x) = 3x^2 + 3, x = 0.7, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2cos(1π((2x - 1)/(3x)) - 3) - 2 and g(x) = -3x^2 + 2x + 1 from x = -0.5 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5(-4x + 4) + 2 and g(x) = (-1x + 1)/(-3x) from x = -0.0 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2e^(1x) - 1))/(-1(-2e^(1x) - 1) - 3) and g(x) = -2x^2 - 2x + 5 between the vertical lines x = 0.4 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(1cos(3πx - 1) - 2) + 1| - 1 and g(x) = -2|x| + 2 between the vertical lines x = -1.3 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(-3cos(2πx + 1)) - 2)/(1(-3cos(2πx + 1)) + 2) and g(x) = (2x + 3)/(1x - 3) from x = 0.1 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(-1e^(-1x) + 2)^2 + 3(-1e^(-1x) + 2) - 1 and g(x) = 5x^2 + 3x from x = -0.5 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(5x^2 + 3x + 4) + 3)/(-2(5x^2 + 3x + 4) + 1) and g(x) = 1x^2 - 3x - 2 between the vertical lines x = 0.0 and x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2cos(1π(-1|x + 3| - 2) - 2) + 3, g(x) = (2x + 1)/(2x + 2), x = -4.5, and x = -4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3sin(3π((1x + 2)/(3x + 1)) - 1) and g(x) = -2x + 4 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(2π(-1|x| + 2) - 3) + 2 and g(x) = 3|x - 2| + 2 between the vertical lines x = 1.8 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(-4x^2 - 2x - 1)^2 - 3(-4x^2 - 2x - 1) + 2, g(x) = 5x^2 + 1x - 5, x = -0.9, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1x^2 + 1) - 3)/(3(1x^2 + 1) - 2) and g(x) = 1|x + 3| - 1 between the vertical lines x = -5.0 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-5x^2 - 5x + 5) - 2)/(2(-5x^2 - 5x + 5)) and g(x) = -5x + 1 between the vertical lines x = -1.6 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(2x - 3) - 2)/(2(2x - 3) + 1) and g(x) = 3|x + 1| - 2 from x = -1.5 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(-1sin(3πx)))/(3(-1sin(3πx)) - 2) and g(x) = -1x + 5 from x = -2.9 to x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1cos(1π(-5x - 1) + 1), g(x) = (-1x + 1)/(2x + 2), x = 3.4, and x = 3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2cos(2π(1x^2 + 5x - 2) + 2) and g(x) = (-3x - 3)/(1x - 3) from x = -4.8 to x = -4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -5(1cos(3πx + 3) + 1) - 5 and g(x) = 3x + 4 from x = -3.9 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|(1cos(3πx + 2) - 3) + 3| + 2, g(x) = (-1x + 2)/(2x + 3), x = -0.7, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(-1e^(-2x) + 2) + 1)/(1(-1e^(-2x) + 2)), g(x) = (1x - 2)/(-2x + 3), x = -0.2, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3((-1x + 1)/(-3x + 4))^2 - 5((-1x + 1)/(-3x + 4)) - 4, g(x) = (-2x + 3)/(-2x + 3), x = 1.2, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-1cos(3πx + 2)) + 2)/(1(-1cos(3πx + 2))) and g(x) = -2|x + 2| - 3 between the vertical lines x = 3.0 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2((-3x - 2)/(-2x - 3)) - 4 and g(x) = (2x - 2)/(3x - 2) from x = -1.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4((2x)/(1x + 1)) + 5 and g(x) = (-2x + 2)/(-3x + 1) from x = -0.3 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(2sin(1πx) - 1) + 1)/(-2(2sin(1πx) - 1) + 1) and g(x) = 4x^2 + 5x + 2 from x = -1.2 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(-3x^2 - 2x - 3))/(-3(-3x^2 - 2x - 3) + 4), g(x) = 1|x + 2| - 2, x = -3.7, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(-3x^2 + 5x)^2 - 4(-3x^2 + 5x) - 2 and g(x) = 1x - 5 from x = -0.7 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(3sin(1πx - 2) + 3)|, g(x) = -5x + 2, x = -1.2, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|(-1sin(2πx + 3) - 2)| + 3, g(x) = 2|x - 2| - 2, x = 3.1, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
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