messages listlengths 1 1 | ground_truth stringlengths 3 8 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2|(-3e^(-1(-4((1x + 2)/(2x - 1))^2 + 2((1x + 2)/(2x - 1)) - 5)) - 1) + 1| + 3 and g(x) = 4(-5((-2x + 2)/(-3x - 3))^2 - 1((-2x + 2)/(-3x - 3)) - 4) + 4 from x = -1.2 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex forma... | -1200.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1((-1(1|(-1x + 2) - 3|))/(3(1|(-1x + 2) - 3|) - 2))^2 - 2((-1(1|(-1x + 2) - 3|))/(3(1|(-1x + 2) - 3|) - 2)) - 4 and g(x) = -4(-3|(1x + 5)| + 2)^2 + 3(-3|(1x + 5)| + 2) + 1 from x = -4.8 to x = -4.1. Round to 1 decimal place.\n\nPresent the a... | 2.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|((-2(-5x^2 + 1x - 5) + 1)/(-2(-5x^2 + 1x - 5) - 2)) - 1| + 3 and g(x) = 1|(2sin(3πx - 3) - 2) - 2| - 1 from x = -4.7 to x = -4.4. Round 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) = (2(4(2sin(2πx + 1))^2 - 4(2sin(2πx + 1)) + 5) - 1)/(-1(4(2sin(2πx + 1))^2 - 4(2sin(2πx + 1)) + 5) - 3) and g(x) = 3cos(3π(1|x - 2| - 2) - 1) - 3 between the vertical lines x = 1.8 and x = 2.2. Round to 1 decimal place.\n\nPresent th... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|((-2(-2sin(3πx + 1) + 3) + 3)/(-1(-2sin(3πx + 1) + 3) + 2)) + 1| - 2 and g(x) = -1(3x)^2 - 2(3x) + 4 from x = 0.2 to x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(-2(3sin(1πx + 3) - 1) + 2) - 2)/(1(-2(3sin(1πx + 3) - 1) + 2) - 3), g(x) = 2|(-2sin(1πx + 3) + 2) + 1| + 1, x = 1.0, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 4.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3sin(2π(4((-1x + 3)/(2x - 3)) + 5) - 1) + 3 and g(x) = 2|(-3x + 4) + 1| - 3 from x = 0.5 to x = 0.6. 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) = -5((3(-3|(1x^2 - 4x - 5) - 1| + 1) - 1)/(-1(-3|(1x^2 - 4x - 5) - 1| + 1) - 1)), g(x) = -3|(-5(2cos(1πx + 1) + 1) - 4) + 2| + 1, x = -1.2, and x = -1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your... | 0.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3(3sin(1π((2x)/(1x + 1)) - 1)) - 4 and g(x) = (1(-3x^2 - 3x + 4) - 2)/(-1(-3x^2 - 3x + 4) + 2) from x = -0.9 to x = -0.8. Round 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) = 4((2(-2|x + 2| + 3) + 1)/(2(-2|x + 2| + 3))) - 5 and g(x) = 1cos(1π(-4x + 1) - 3) + 1 from x = -2.8 to x = -2.7. 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(-4(-2|x - 2| - 2)^2) + 1 and g(x) = -2e^(-2((2x + 3)/(-2x - 2))) - 3 from x = 1.7 to x = 2.2. Round 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) = (-2(4(-1x - 3)^2 - 4(-1x - 3)) - 1)/(-1(4(-1x - 3)^2 - 4(-1x - 3)) + 2), g(x) = -3(-3cos(3πx + 2) - 3) + 2, x = 4.1, and x = 4.199999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2|(-1e^(1x) - 1) - 2| - 3) - 1)/(-2(2|(-1e^(1x) - 1) - 2| - 3) - 3) and g(x) = -3|(-3sin(2πx + 1) + 2)| between the vertical lines x = -1.0 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(2|(-5x^2 - 3x + 4) + 1| - 1) - 2 and g(x) = 2sin(1π(5x - 5) - 3) + 3 from x = -1.0 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(3((2x + 2)/(2x + 3))^2 + 1) + 1, g(x) = -1e^(1(-1x + 2)) - 3, x = -1.4, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3|(-3sin(1πx + 1) + 3) + 3| + 3) - 5 and g(x) = 2|(-2cos(2πx + 3) - 2) - 2| + 3 between the vertical lines x = 3.5 and x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 7.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-5(2cos(2π((3x + 2)/(1x + 3)) - 2) + 1)^2 + 3(2cos(2π((3x + 2)/(1x + 3)) - 2) + 1)) - 4 and g(x) = 2e^(-2(1((2x - 2)/(1x + 1))^2 - 2((2x - 2)/(1x + 1)) + 3)) - 2 between the vertical lines x = -2.2 and x = -2.1. Round to 1 decima... | 1.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1((-2(-2(-2|x - 2| + 2) - 1))/(-1(-2(-2|x - 2| + 2) - 1) - 1))^2 + 5((-2(-2(-2|x - 2| + 2) - 1))/(-1(-2(-2|x - 2| + 2) - 1) - 1)) + 4, g(x) = (-3(-2|(-4x + 1) - 1| + 2) + 2)/(-2(-2|(-4x + 1) - 1| + 2) - 1), x = 0.3, and x = 0.8. Round your ... | 8.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2sin(3π(-2|((3x + 3)/(2x - 1)) + 2| - 1) + 1), g(x) = 2sin(2π(1|x| + 3) + 1), 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"
}
] | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-1e^(-1(-2|x| + 1)) + 2) - 1)/(-1(-1e^(-1(-2|x| + 1)) + 2) + 2), g(x) = (1(1x - 3) + 3)/(2(1x - 3) + 3), x = 0.8, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 31.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(2|(1sin(3πx - 1) - 1)|)^2 - 1(2|(1sin(3πx - 1) - 1)|) + 2, g(x) = 1e^(-1(3|x + 3| - 3)) - 3, x = -0.9, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 3.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(2cos(2π((1(-2|x + 3| + 2) - 2)/(1(-2|x + 3| + 2) - 3)) - 1) + 1) - 3, g(x) = 2(-4(-2e^(1x) + 3) - 1)^2 + 3(-4(-2e^(1x) + 3) - 1) - 5, x = 0.3, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\box... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(-1|(5(2sin(1πx + 3) - 3) - 2) + 2| + 2)^2 - 5(-1|(5(2sin(1πx + 3) - 3) - 2) + 2| + 2), g(x) = 5((-3(4x - 1) - 3)/(3(4x - 1) - 1))^2 + 1((-3(4x - 1) - 3)/(3(4x - 1) - 1)) - 1, x = 0.3, and x = 0.4. Round your answer to 1 decimal place.\n\nP... | -63.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1(-2sin(1π(-2x - 2) - 3) + 2)^2 + 2(-2sin(1π(-2x - 2) - 3) + 2) - 1, g(x) = (-3(-2|x + 2| + 1))/(-1(-2|x + 2| + 1) + 3), x = 2.4, and x = 3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 7.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(-5((-1x - 1)/(-1x)) - 5)^2 + 1(-5((-1x - 1)/(-1x)) - 5) - 3 and g(x) = 3(1|x - 2| - 3) - 2 from x = -0.5 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(3(-2|((-3x + 3)/(3x - 1)) - 2| + 2)^2 + 5(-2|((-3x + 3)/(3x - 1)) - 2| + 2) - 1) + 5 and g(x) = -1e^(-1(1|((2x - 2)/(1x + 1)) + 1| - 1)) - 3 from x = 0.7 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3((3(5(-3|x - 1|) + 1) + 2)/(-1(5(-3|x - 1|) + 1) - 3))^2 + 4((3(5(-3|x - 1|) + 1) + 2)/(-1(5(-3|x - 1|) + 1) - 3)) + 4 and g(x) = -4(-3cos(2π((1x - 1)/(-1x - 2)) + 3) + 1) - 3 from x = 0.8 to x = 1.2. Round to 1 decimal place.\n\nPresent t... | 7.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2e^(1((-1(3|x + 3| + 1) - 2)/(-2(3|x + 3| + 1) - 2))) + 1)^2 + 2(-2e^(1((-1(3|x + 3| + 1) - 2)/(-2(3|x + 3| + 1) - 2))) + 1) + 5 and g(x) = (2(2sin(2π(4x^2 + 1x + 1) - 3) + 1) - 3)/(-1(2sin(2π(4x^2 + 1x + 1) - 3) + 1) + 2) betwe... | 1.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2((1(-1|x + 3| + 3) - 1)/(-1(-1|x + 3| + 3) - 3)) + 3 and g(x) = -4(3|x + 2| - 2) from x = -2.4 to x = -1.6. 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) = 1(1sin(2π(1x + 1) + 3) + 3)^2 + 4(1sin(2π(1x + 1) + 3) + 3) - 5, g(x) = (3(-1cos(1πx)) - 1)/(-1(-1cos(1πx))), x = 1.5, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 34.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|(2e^(1((1(-5x^2 + 4x - 3) + 3)/(-3(-5x^2 + 4x - 3) + 2))) - 1) + 1| + 1, g(x) = -1|(1(-3x - 1)^2 + 2(-3x - 1) + 2) - 3| + 3, x = -0.9, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 7.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-2(2|x - 3| - 3)^2 - 3(2|x - 3| - 3) + 5) - 2)/(-3(-2(2|x - 3| - 3)^2 - 3(2|x - 3| - 3) + 5) + 1) and g(x) = 5(1|x + 2| + 3) + 2 between the vertical lines x = 1.0 and x = 2.7. Round to 1 decimal place.\n\nPresent the answer in L... | 63.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(1(2cos(2π(1x^2 + 3x + 1) - 1) - 2) + 4) - 2| + 3 and g(x) = (1(-3(-3cos(2πx - 2) + 3) - 3) - 2)/(1(-3(-3cos(2πx - 2) + 3) - 3) + 1) from x = 2.9 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(-5(1|(2e^(1x)) + 3| + 3)^2 + 2(1|(2e^(1x)) + 3| + 3) - 5) + 3)/(1(-5(1|(2e^(1x)) + 3| + 3)^2 + 2(1|(2e^(1x)) + 3| + 3) - 5)) and g(x) = -2|((-1(-4x + 1) - 2)/(2(-4x + 1) + 2)) - 2| + 1 from x = 0.5 to x = 0.8. Round to 1 decimal place.\n... | 5.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3|(1((1x - 2)/(1x - 3))^2 + 1((1x - 2)/(1x - 3)) + 1) - 1| + 3, g(x) = 1(-5x + 4)^2 + 2(-5x + 4) - 4, x = 0.6, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 3.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(1sin(3π(-2(5x - 4)^2 - 5(5x - 4) + 2) - 2)) - 2| - 2, g(x) = -3cos(2π(-1|(1x^2 - 4x - 4) + 1| + 1) + 2), x = -4.8, and x = -4.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(1|((1x + 2)/(-1x)) + 3| - 3)^2 + 3(1|((1x + 2)/(-1x)) + 3| - 3) + 5 and g(x) = -4(3cos(2πx - 3) - 3) + 4 from x = -1.6 to x = -1.4. 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) = -5((3(3cos(1π(2|x - 3| + 3) + 1)))/(3(3cos(1π(2|x - 3| + 3) + 1)) + 3)) + 2, g(x) = -2(-3|((-2x - 2)/(-3x - 3)) - 2| + 2), x = -0.1, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 11.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -4(-3sin(1π(-3|x - 2| + 2) + 3)) + 5 and g(x) = (-1(1cos(1πx - 2) + 3) - 1)/(3(1cos(1πx - 2) + 3)) from x = -2.6 to x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(1e^(-1((-1x + 2)/(-3x + 4))) + 2)^2 + 4(1e^(-1((-1x + 2)/(-3x + 4))) + 2) - 4, g(x) = -3|(-3sin(2πx - 1) - 1) - 2| - 2, x = 2.7, and x = 3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 1.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3cos(2π((3(3|x - 1| - 2) - 1)/(2(3|x - 1| - 2) + 1))) and g(x) = -3(1|x| + 1) + 1 between the vertical lines x = 0.2 and x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(-3(3|(-3x^2 - 4x + 1) + 3| - 2)) - 2)/(-2(-3(3|(-3x^2 - 4x + 1) + 3| - 2)) + 1) and g(x) = -2(2|((2x)/(-3x + 1)) + 2|) - 5 from x = -2.1 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 48.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((2(1|(4x - 1) + 3|))/(2(1|(4x - 1) + 3|) - 1))^2 + 5 and g(x) = 1((-2(2x - 2) - 2)/(-3(2x - 2)))^2 + 4((-2(2x - 2) - 2)/(-3(2x - 2))) + 1 between the vertical lines x = 1.0 and x = 1.4. Round to 1 decimal place.\n\nPresent the ans... | 24.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3(2sin(2πx + 3) - 2) - 4)^2 - 5(-3(2sin(2πx + 3) - 2) - 4) - 2 and g(x) = -2(1e^(-1x) - 3) - 2 between the vertical lines x = -1.1 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 0.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π(1|((-2x + 3)/(-2x - 2)) - 3| - 3) - 2) - 2 and g(x) = 2sin(2π(1x - 5) + 3) between the vertical lines x = -0.8 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(3((3(3sin(3πx + 1)) - 3)/(-2(3sin(3πx + 1)) + 3))^2 + 3((3(3sin(3πx + 1)) - 3)/(-2(3sin(3πx + 1)) + 3)) + 2) - 4 and g(x) = (-2(-2|(3x^2 + 2x)| - 2))/(-3(-2|(3x^2 + 2x)| - 2) - 2) from x = -3.1 to x = -3.0. Round to 1 decimal place.\n\nPre... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4((2(1cos(2π(-4x)) - 1))/(-1(1cos(2π(-4x)) - 1) - 3))^2 - 5((2(1cos(2π(-4x)) - 1))/(-1(1cos(2π(-4x)) - 1) - 3)) - 1, g(x) = -5((-3(3sin(3πx + 2) + 2) - 1)/(-3(3sin(3πx + 2) + 2) - 2)) - 4, x = 1.2, and x = 1.3. Round your answer to 1 decima... | 0.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(-2|((2x + 1)/(-2x - 2))| + 2) + 3, g(x) = -1(-2e^(1x) + 2)^2 - 5(-2e^(1x) + 2) - 3, x = 0.3, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2sin(3π(-3(-2|((1x)/(-3x - 2)) - 1| - 1)^2 - 3(-2|((1x)/(-3x - 2)) - 1| - 1)) - 3) - 3, g(x) = 1(4((3x + 2)/(1x)) + 5)^2 - 2(4((3x + 2)/(1x)) + 5) - 5, x = -0.5, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in L... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3((2(1|x + 1| - 3) + 1)/(1(1|x + 1| - 3)))^2 + 5((2(1|x + 1| - 3) + 1)/(1(1|x + 1| - 3))) + 3 and g(x) = 4(2|x + 2|) - 2 from x = -3.8 to x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 3.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5((-2(1(1|x| - 1) + 4) + 3)/(-2(1(1|x| - 1) + 4) + 1))^2 - 3((-2(1(1|x| - 1) + 4) + 3)/(-2(1(1|x| - 1) + 4) + 1)) - 3 and g(x) = 1|((-1(2cos(3πx - 1)) + 1)/(2(2cos(3πx - 1)) - 1)) + 2| - 2 from x = 4.6 to x = 4.9. Round to 1 decimal place.\n... | 0.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(1((2(-3sin(2πx + 1) - 2))/(-1(-3sin(2πx + 1) - 2) + 3)) - 3)^2 + 5(1((2(-3sin(2πx + 1) - 2))/(-1(-3sin(2πx + 1) - 2) + 3)) - 3) - 2 and g(x) = (2(2|(4x^2 - 3x - 2) - 2| - 2))/(2(2|(4x^2 - 3x - 2) - 2| - 2) - 3) from x = -0.9 to x = -0.5. R... | 4.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2|(2x + 3) + 1| - 2)^2 - 1(2|(2x + 3) + 1| - 2) + 2 and g(x) = 1cos(2π(-3x^2 - 4x - 5) + 3) + 3 between the vertical lines x = -1.6 and x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|((-2(4(-4x - 5)^2 - 3(-4x - 5) - 3) - 1)/(1(4(-4x - 5)^2 - 3(-4x - 5) - 3))) - 1| - 3, g(x) = (1(1|(-3x + 2) - 1| + 2) + 3)/(-3(1|(-3x + 2) - 1| + 2) - 1), x = -1.6, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer... | 2.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(1|((2(1e^(2x) - 3) + 1)/(-2(1e^(2x) - 3) - 3)) + 2| + 1) + 2, g(x) = 3((2(2|x - 1| - 2) - 1)/(1(2|x - 1| - 2) - 3))^2 - 5((2(2|x - 1| - 2) - 1)/(1(2|x - 1| - 2) - 3)) - 4, x = -0.7, and x = 2.7. Round your answer to 1 decimal place.\n\nPre... | 47.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(2(-3|(-3e^(2x) + 1) - 3| - 3) + 2) - 2)/(3(2(-3|(-3e^(2x) + 1) - 3| - 3) + 2) - 2) and g(x) = 1|(2(-4x - 1)^2 + 3(-4x - 1) - 2) - 3| - 2 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{You... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-3(1|x + 3| - 1)^2 + 5(1|x + 3| - 1) + 2) + 2)/(-1(-3(1|x + 3| - 1)^2 + 5(1|x + 3| - 1) + 2) - 1) and g(x) = -2|(-2x + 2) + 1| - 3 between the vertical lines x = -3.5 and x = -2.5. Round to 1 decimal place.\n\nPresent the answer ... | 17.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(1π(-2|(-3x^2 + 4x + 2) + 2| - 2) - 3) - 1 and g(x) = 3|(-3cos(1πx - 3))| - 3 between the vertical lines x = -3.7 and x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": ... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(1cos(3π((3x + 3)/(-1x + 2)) - 2) + 1) + 1| - 1 and g(x) = (-2(2|x + 2| - 1) - 2)/(3(2|x + 2| - 1) + 2) from x = -2.1 to x = -1.9. 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) = -4(1(2|x| + 1)^2 - 2(2|x| + 1) - 1) and g(x) = -1(1e^(-2x) - 2)^2 + 4(1e^(-2x) - 2) - 1 between the vertical lines x = -1.0 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 1.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2cos(2π(1|(1x^2 - 5x + 5) + 2| + 3) + 3) + 3, g(x) = (-2(-3x + 3) - 2)/(-1(-3x + 3) + 3), x = 3.4, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(2((2x - 1)/(2x)) + 3) + 1| + 2, g(x) = (2(2|x + 2| - 2) - 2)/(2(2|x + 2| - 2) + 3), x = -2.2, and x = -1.8. Round your answer 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) = 4((1(-2|x - 2| - 2))/(-2(-2|x - 2| - 2) - 3))^2 - 2, g(x) = (-3(1cos(3πx + 1) + 1) - 3)/(-3(1cos(3πx + 1) + 1) + 1), x = 2.4, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-1((-1x + 1)/(-2x)) + 4) - 2| + 3 and g(x) = 2|(1x^2 - 5x - 4) - 3| between the vertical lines x = -1.3 and x = -1.0. 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) = 4(-2((-2(1sin(3πx + 1) - 2) + 2)/(-1(1sin(3πx + 1) - 2) - 3)) + 1)^2 + 4(-2((-2(1sin(3πx + 1) - 2) + 2)/(-1(1sin(3πx + 1) - 2) - 3)) + 1) - 1 and g(x) = 2(3(2|x - 3| - 1)^2 + 2) - 3 between the vertical lines x = -1.4 and x = -1.2. ... | 37.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(2cos(3π((3(3|x| + 1) - 1)/(-3(3|x| + 1) + 2)) - 3) - 1) + 3 and g(x) = 2(-1|(-1x + 5) - 2| - 1)^2 - 3(-1|(-1x + 5) - 2| - 1) - 1 between the vertical lines x = 2.9 and x = 3.1. Round to 1 decimal place.\n\nPresent the answer in La... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(3|(5x^2 - 3x - 2) + 2|) + 2)/(-2(3|(5x^2 - 3x - 2) + 2|) + 1), g(x) = 3(-3x)^2 + 2(-3x) + 4, x = -0.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 1.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((2(-2x^2 + 1x + 5) - 1)/(-2(-2x^2 + 1x + 5) + 3)) - 2| - 2 and g(x) = -1e^(1(-1x^2 - 3x)) between the vertical lines x = -2.0 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 2.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2sin(2π(-2|((-1(4x + 1) - 1)/(-3(4x + 1) - 2)) + 3| + 2) - 1) + 1, g(x) = 2e^(2(-2|(-1x^2 - 5x - 5)| - 1)) - 1, x = -0.4, and x = -0.30000000000000004. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{You... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-4((3x - 2)/(-1x - 1))^2 + 5((3x - 2)/(-1x - 1)) - 3) + 2| and g(x) = -1(-1e^(2x))^2 - 2(-1e^(2x)) + 5 between the vertical lines x = 0.0 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 2.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(2π((-3(-1x^2 + 3) + 2)/(-3(-1x^2 + 3) - 1)) - 3) - 2 and g(x) = (1(1x - 4))/(3(1x - 4) - 2) between the vertical lines x = -1.7 and x = -1.5999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\box... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(5((3(-3cos(1πx + 2) + 1))/(-1(-3cos(1πx + 2) + 1) + 2))^2 - 4((3(-3cos(1πx + 2) + 1))/(-1(-3cos(1πx + 2) + 1) + 2))) + 3 and g(x) = (1(-1e^(2(-4x^2 - 2x)) - 1) - 1)/(-1(-1e^(2(-4x^2 - 2x)) - 1) - 2) between the vertical lines x =... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4((1(2|(-2cos(1πx + 2) - 2) + 3| + 1) - 2)/(1(2|(-2cos(1πx + 2) - 2) + 3| + 1) + 2))^2 + 4((1(2|(-2cos(1πx + 2) - 2) + 3| + 1) - 2)/(1(2|(-2cos(1πx + 2) - 2) + 3| + 1) + 2)) + 4, g(x) = 2e^(-1((1(-1|x + 1| - 1) - 2)/(3(-1|x + 1| - 1)))) + 2,... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((1(-2|x + 2|))/(-2(-2|x + 2|)))^2 - 1((1(-2|x + 2|))/(-2(-2|x + 2|))) + 1 and g(x) = (1(2cos(3πx + 1) + 1))/(-3(2cos(3πx + 1) + 1) - 1) between the vertical lines x = -0.3 and x = 0.1. Round to 1 decimal place.\n\nPresent the ans... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1|(-5(-1(-3sin(1πx + 1) + 3)^2 + 4(-3sin(1πx + 1) + 3) - 5)) + 3| - 2 and g(x) = -5((-3(-2|x - 3| + 3) + 3)/(3(-2|x - 3| + 3) - 2)) + 5 from x = 2.7 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 43.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-3e^(2(3x - 5)) + 2) - 1)/(3(-3e^(2(3x - 5)) + 2)) and g(x) = -1(-1x - 4)^2 - 3(-1x - 4) + 2 between the vertical lines x = -0.2 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 9.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((-3(-4x^2 - 3x + 4) - 2)/(-2(-4x^2 - 3x + 4) - 2)) - 1 and g(x) = 2(-4x^2 - 3x - 2) + 2 between the vertical lines x = -1.5 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 22.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(1(1|(-3x - 1) + 2| - 2)^2 - 1(1|(-3x - 1) + 2| - 2) - 3) - 2)/(1(1(1|(-3x - 1) + 2| - 2)^2 - 1(1|(-3x - 1) + 2| - 2) - 3) + 2) and g(x) = 4(-1|((-3x + 1)/(1x)) + 3| - 3) between the vertical lines x = -0.8 and x = -0.1. Round to... | 23.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(-1(3((-3x + 2)/(2x))^2 - 4((-3x + 2)/(2x)) + 2) - 5) - 3| - 3, g(x) = (-3(2|(-2x^2 + 4x + 4) + 1| + 1) + 2)/(-1(2|(-2x^2 + 4x + 4) + 1| + 1) + 3), x = -1.0, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTe... | 39.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-1(-3|x - 1| + 3) + 3)/(-2(-3|x - 1| + 3) - 1))^2 + 2((-1(-3|x - 1| + 3) + 3)/(-2(-3|x - 1| + 3) - 1)) - 1 and g(x) = 2(-2sin(2πx + 3) - 3)^2 + 1(-2sin(2πx + 3) - 3) + 2 between the vertical lines x = -0.1 and x = 2.1. Round to 1... | 47.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-1(-1(2sin(3πx + 3) - 1)^2 - 4(2sin(3πx + 3) - 1) + 3) - 1) + 2)/(1(-1(-1(2sin(3πx + 3) - 1)^2 - 4(2sin(3πx + 3) - 1) + 3) - 1)) and g(x) = 2|(-1((-2x + 3)/(-2x - 3))^2 - 3((-2x + 3)/(-2x - 3)) + 4) - 3| + 3 between the vertical... | 1.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1(-3|x + 3| + 2) + 2)^2 + 3(-1(-3|x + 3| + 2) + 2) - 1 and g(x) = (-1(1|x - 3| + 3) + 1)/(1(1|x - 3| + 3)) between the vertical lines x = -4.0 and x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxe... | 1.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|((2(-1(4x^2 - 2x + 4) - 4) + 3)/(3(-1(4x^2 - 2x + 4) - 4) - 2)) - 2| + 3, g(x) = 3e^(1((-1(-4x^2 + 4x + 2))/(-3(-4x^2 + 4x + 2) - 2))), x = -0.4, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\... | 4.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(-4(-5x^2 + 5x) + 3) - 2|, g(x) = -3cos(2π(-1|x + 2| - 3) - 2) - 2, x = 0.0, and x = 0.1. 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) = -1(-1(2|x + 1| - 1) - 1)^2 - 5(-1(2|x + 1| - 1) - 1) + 2 and g(x) = 4((-3x - 2)/(-1x + 2))^2 - 2((-3x - 2)/(-1x + 2)) - 5 between the vertical lines x = -3.5 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex form... | 31.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-2e^(2(3|((-2x - 2)/(-1x)) + 1| - 2)) + 1) - 3 and g(x) = 3cos(1π(5((-3x + 3)/(2x + 1))^2 + 3((-3x + 3)/(2x + 1)) - 4) + 3) - 3 between the vertical lines x = -0.8 and x = -0.7000000000000001. Round to 1 decimal place.\n\nPresent ... | 0.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1((-1(-2(-2|x - 1| - 1)^2 - 1(-2|x - 1| - 1) + 4))/(-1(-2(-2|x - 1| - 1)^2 - 1(-2|x - 1| - 1) + 4) + 3)) + 5 and g(x) = -2cos(1π((-3(4x + 4) - 3)/(-3(4x + 4) + 1)) - 3) + 1 from x = 0.9 to x = 1.1. Round to 1 decimal place.\n\nPresent the an... | 21.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(2(-3(-1|x - 3| + 3))^2 + 3(-3(-1|x - 3| + 3)) - 1) + 2)/(-1(2(-3(-1|x - 3| + 3))^2 + 3(-3(-1|x - 3| + 3)) - 1) + 2), g(x) = (2(-1(-3|x - 1| - 1)^2 - 4(-3|x - 1| - 1) + 1) - 1)/(-1(-1(-3|x - 1| - 1)^2 - 4(-3|x - 1| - 1) + 1) + 2), x = -0.0... | 18.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1cos(3π(-5(-3((-3x - 1)/(-2x - 3))^2 - 1) - 1) - 1) - 3, g(x) = -2sin(3π(1|(-5x - 4) - 3| - 3) - 1) - 1, 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": "u... | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3cos(2π(-2((-1x - 1)/(-2x - 3))^2 - 4((-1x - 1)/(-2x - 3)) - 3) - 2), g(x) = -2(3|x + 1| - 3)^2 - 4(3|x + 1| - 3) - 4, x = -1.6, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(2cos(1π(-1|((1x - 2)/(-3x - 3)) + 1|) + 1) - 3)^2 - 4(2cos(1π(-1|((1x - 2)/(-3x - 3)) + 1|) + 1) - 3) + 3 and g(x) = 2(1cos(3π((2x - 2)/(-2x + 1)) - 1) + 2)^2 - 5(1cos(3π((2x - 2)/(-2x + 1)) - 1) + 2) + 1 between the vertical lin... | 0.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3π(4(-5(-1|x - 3| - 3) + 5)^2 + 1(-5(-1|x - 3| - 3) + 5)) - 1) and g(x) = 2(3e^(2((-1x + 1)/(2x - 3))) - 2) - 4 between the vertical lines x = 1.1 and x = 1.2000000000000002. Round to 1 decimal place.\n\nPresent the answer in L... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1(-3sin(1πx + 1)) + 3)^2 - 1(-1(-3sin(1πx + 1)) + 3) - 1 and g(x) = -2cos(1π((3x + 3)/(1x + 3)) + 2) - 2 between the vertical lines x = -3.0 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-4(3x^2 - 5x + 2) + 3))/(-2(-4(3x^2 - 5x + 2) + 3) - 1), g(x) = -1((-1x - 3)/(3x + 3)) + 1, x = 0.2, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 2.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(1(-1(1((-3x - 2)/(3x + 2))^2 - 4((-3x - 2)/(3x + 2)) + 1) + 5)) - 1 and g(x) = -2sin(2π(5((3x + 1)/(-3x + 2))^2 + 3((3x + 1)/(-3x + 2)) + 2)) between the vertical lines x = 1.8 and x = 1.9. Round to 1 decimal place.\n\nPresent t... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|((-2(5x - 3) - 3)/(2(5x - 3) + 2)) + 3| - 2, g(x) = -2(-2x + 1)^2 + 4(-2x + 1) - 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}",
"role": "user"
}
] | 2.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1|((2x - 2)/(-3x - 2)) + 1| - 2)^2 - 3(-1|((2x - 2)/(-3x - 2)) + 1| - 2) - 3 and g(x) = -3(-2cos(1πx - 3) - 1)^2 - 2(-2cos(1πx - 3) - 1) - 5 between the vertical lines x = 3.4 and x = 3.8. Round to 1 decimal place.\n\nPresent th... | 1.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3cos(3π(-1((3x)/(-1x))^2 - 3((3x)/(-1x)) + 5) + 2), g(x) = 3|(3x) + 3| - 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}",
"role": "user"
}
] | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(1(2sin(2π(-1|x - 1| + 2) + 2) + 2) - 5)^2 + 1(1(2sin(2π(-1|x - 1| + 2) + 2) + 2) - 5) - 5, g(x) = 3(2((1x + 1)/(-1x + 2))^2 + 5((1x + 1)/(-1x + 2)) - 5) + 5, x = -2.0, and x = -1.1. Round your answer to 1 decimal place.\n\nPresent the ans... | 29.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(1(-1|x - 3| + 3) + 5) - 1)/(-1(1(-1|x - 3| + 3) + 5) + 3), g(x) = -2|(3sin(1πx + 3) - 2) - 3| + 3, x = 1.9, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 6.3 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.