messages listlengths 1 1 | ground_truth stringlengths 3 8 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3(-2cos(3π(3|x - 2| - 2) + 1) - 3)^2 + 3(-2cos(3π(3|x - 2| - 2) + 1) - 3) - 3 and g(x) = -1|(-1e^(1x) + 2) - 1| + 2 from x = -5.0 to x = -4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 0.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((1(-3(1|x + 1|) + 3) + 2)/(-1(-3(1|x + 1|) + 3) - 2))^2 - 3((1(-3(1|x + 1|) + 3) + 2)/(-1(-3(1|x + 1|) + 3) - 2)) - 5 and g(x) = -2cos(1π(-1(-1|x + 1|) - 4) - 2) + 2 between the vertical lines x = -1.3 and x = -0.7. Round to 1 dec... | 0.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(-4(-3|(5x^2 - 1x - 3) + 1| + 1) - 5) - 2)/(-1(-4(-3|(5x^2 - 1x - 3) + 1| + 1) - 5) + 2), g(x) = 3sin(2π(-1(-3|x| + 1) - 4)) - 3, x = -4.7, and x = -4.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 0.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3|(5(-3cos(3πx + 3) - 1) - 3) - 3| - 1 and g(x) = (3(-2sin(1πx - 2)) + 3)/(-3(-2sin(1πx - 2)) - 1) from x = 0.8 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5(-3|(-2cos(1π(-5x^2 + 5x - 4) + 3) + 3) + 1| - 1) - 2 and g(x) = (2(2cos(1π(-2x^2 - 2x)) + 3) + 1)/(2(2cos(1π(-2x^2 - 2x)) + 3) - 3) from x = -3.3 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your an... | 13.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3((-2(2|x + 1| - 1))/(-3(2|x + 1| - 1) + 1)) + 1 and g(x) = 4(-2sin(3πx + 3) + 2) + 3 from x = -1.6 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(3cos(1π(3x - 3) - 1) + 2) - 2)/(3(3cos(1π(3x - 3) - 1) + 2)) and g(x) = -1(-1x^2 - 1x - 4) + 4 from x = -4.5 to x = -4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-4(-5(1sin(1πx + 2) + 1) + 2)^2 + 4(-5(1sin(1πx + 2) + 1) + 2) - 3) + 2)/(-2(-4(-5(1sin(1πx + 2) + 1) + 2)^2 + 4(-5(1sin(1πx + 2) + 1) + 2) - 3) - 3) and g(x) = 4(3((-1x - 2)/(2x + 3))^2 - 5((-1x - 2)/(2x + 3)) - 1) + 1 from x = -2.1 to x... | 2.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-1e^(1(-3|x + 1| + 2)) - 3) + 1)/(-2(-1e^(1(-3|x + 1| + 2)) - 3) + 3), g(x) = 2|(-2cos(1πx + 2) - 1) - 1| - 2, x = -2.0, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 1.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(-1sin(3π(-4x^2 - 5x)) + 3) - 1)/(2(-1sin(3π(-4x^2 - 5x)) + 3) + 1), g(x) = (-2(4x - 4) + 3)/(-1(4x - 4) - 1), x = 1.7, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(2((3(3sin(1πx - 2) - 2))/(1(3sin(1πx - 2) - 2) - 2))^2 - 2) - 3, g(x) = -2|((-2(1x^2 + 1x + 3) + 1)/(-2(1x^2 + 1x + 3) - 3)) + 2| + 3, x = -1.0, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\... | 15.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1cos(2π(-1((-1x + 1)/(-2x - 2)) - 1)) + 2, g(x) = 4(-5x - 1)^2 + 5(-5x - 1) - 3, x = -0.4, and x = 0.2. 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) = -1sin(2π((1(-2|x + 3| + 1) - 1)/(-2(-2|x + 3| + 1) + 3)) - 2) + 2 and g(x) = (1(2|x| - 2) - 2)/(3(2|x| - 2) - 2) between the vertical lines x = -1.0 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\box... | 0.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2((-1(-4x + 4) + 1)/(-1(-4x + 4) + 3))^2 + 5((-1(-4x + 4) + 1)/(-1(-4x + 4) + 3)) - 4, g(x) = -2((-1x + 2)/(-1x + 2))^2 + 2((-1x + 2)/(-1x + 2)) - 4, x = 0.4, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex ... | 0.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|((2(-4x + 3) + 1)/(-2(-4x + 3) + 3)) + 2| and g(x) = (1(3sin(1πx + 3) - 3) - 1)/(-1(3sin(1πx + 3) - 3) + 2) from x = -2.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 0.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(1(-2cos(2πx + 3) - 2)^2 + 4(-2cos(2πx + 3) - 2) - 2) - 2, g(x) = 4(2cos(2πx + 2) - 3), x = 4.4, and x = 4.5. 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) = -2|((-1(2e^(-1x) - 1) - 3)/(2(2e^(-1x) - 1))) + 1| + 3 and g(x) = -1|(-1x^2 - 5x) - 1| - 3 between the vertical lines x = 0.4 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 99.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(-2|(-3(-3x + 2)^2 + 4(-3x + 2) - 4) - 3| - 1) + 3)/(2(-2|(-3(-3x + 2)^2 + 4(-3x + 2) - 4) - 3| - 1)) and g(x) = 1sin(2π((1(-3x + 3) + 2)/(-1(-3x + 3))) - 3) - 2 from x = 0.8 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in ... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3sin(1π(-1(2|x + 3| + 2)^2 - 5(2|x + 3| + 2) - 4) + 3) + 2, g(x) = -4(1e^(1x) - 1)^2 + 2(1e^(1x) - 1) + 3, x = -0.5, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-2(3|((-2x + 1)/(-3x + 1)) + 1| + 1) + 2)^2 - 5(-2(3|((-2x + 1)/(-3x + 1)) + 1| + 1) + 2) - 4, g(x) = -1((2(-1x) + 3)/(3(-1x) + 1))^2 - 2((2(-1x) + 3)/(3(-1x) + 1)) - 3, x = 0.4, and x = 0.5. Round your answer to 1 decimal place.\n\nPrese... | 7.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(1(3(1|x - 3|)^2 - 5(1|x - 3|) - 3) - 3) - 3)/(-1(1(3(1|x - 3|)^2 - 5(1|x - 3|) - 3) - 3) - 1) and g(x) = 5(-2|(1x^2 + 3x - 1) + 2| + 1) from x = -2.7 to x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Y... | 0.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-1sin(3π(3|(-3x) - 1| + 1) + 3) - 2)^2 + 5(-1sin(3π(3|(-3x) - 1| + 1) + 3) - 2) - 3 and g(x) = -2(-2e^(-1((-3x + 3)/(-1x + 2))) + 1)^2 + 2(-2e^(-1((-3x + 3)/(-1x + 2))) + 1) - 1 between the vertical lines x = 4.3 and x = 4.4. Roun... | 0.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((-2(-2|x + 2| - 1) + 3)/(1(-2|x + 2| - 1) - 3)) + 1 and g(x) = -1((3x - 3)/(2x - 3)) + 5 between the vertical lines x = -2.3 and x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3(5(-3sin(2π(2|x + 3|) + 1) + 2) + 2)^2 - 2(5(-3sin(2π(2|x + 3|) + 1) + 2) + 2) - 2 and g(x) = (-2(-3|(4x^2 - 1x) + 1| + 1) - 2)/(-2(-3|(4x^2 - 1x) + 1| + 1) + 3) from x = 4.1 to x = 4.199999999999999. Round to 1 decimal place.\n\nPresent th... | 27.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(-2|(3(-2sin(2πx + 3) + 2)^2 + 4(-2sin(2πx + 3) + 2) - 5) + 2|) + 1)/(2(-2|(3(-2sin(2πx + 3) + 2)^2 + 4(-2sin(2πx + 3) + 2) - 5) + 2|) + 2) and g(x) = -1(-2(1cos(2πx + 1) + 1) - 3)^2 + 2(-2(1cos(2πx + 1) + 1) - 3) + 5 from x = 2.6 to x = ... | 14.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(-3|(-1cos(3πx - 2) - 2) - 1| - 1) - 3 and g(x) = 3|(-1e^(2x) + 3) + 2| + 2 from x = 0.7 to x = 1.0. Round 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) = 1|((-1(1x^2 - 4x - 5))/(-2(1x^2 - 4x - 5) - 1)) + 1| + 3, g(x) = (-1(-3sin(2πx - 1) - 2) + 2)/(-2(-3sin(2πx - 1) - 2) - 2), x = -4.9, and x = -4.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 4.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3e^(2(-3(-1x^2 + 4x + 4) - 4)) + 1, g(x) = 1cos(3π(-3|x + 2| - 2) + 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": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3|((2(-2x + 1) - 2)/(1(-2x + 1) - 2)) - 1|)^2 - 4(-3|((2(-2x + 1) - 2)/(1(-2x + 1) - 2)) - 1|) - 5 and g(x) = -1(2cos(1π(-4x - 1) + 2) + 1)^2 + 3(2cos(1π(-4x - 1) + 2) + 1) + 4 between the vertical lines x = 0.2 and x = 1.1. Roun... | 4.4 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(2cos(2π(-5x^2 - 1x - 5) - 2) + 3) - 2)/(-1(2cos(2π(-5x^2 - 1x - 5) - 2) + 3) - 3) and g(x) = (2(-3x^2 - 5x + 1))/(1(-3x^2 - 5x + 1) - 3) between the vertical lines x = -2.2 and x = -2.1. Round to 1 decimal place.\n\nPresent the ... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-1((-2(-5x - 5) - 2)/(-2(-5x - 5) - 1))^2 - 5((-2(-5x - 5) - 2)/(-2(-5x - 5) - 1)) + 3) + 3| + 1 and g(x) = 1cos(3π(-2|((-1x - 3)/(3x + 3)) - 3| + 1) + 2) + 2 between the vertical lines x = 0.8 and x = 3.4. Round to 1 decimal pla... | 2.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-3(1|(2x^2 + 1x + 2)| - 3) + 1)/(-1(1|(2x^2 + 1x + 2)| - 3) + 2), g(x) = (2(-1e^(2x) + 2) + 2)/(2(-1e^(2x) + 2) - 3), x = -1.8, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 93.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3|(-3(1((-1x + 3)/(-1x + 2))^2 + 1((-1x + 3)/(-1x + 2)) - 2) - 3) - 2| + 3 and g(x) = (2(2(-1|x - 3| - 3) + 5))/(-3(2(-1|x - 3| - 3) + 5) - 3) from x = 2.8 to x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed... | 18.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3((2(-5x^2 - 5x - 1) - 3)/(-2(-5x^2 - 5x - 1))) - 4, g(x) = 2|(-3x^2 - 2x + 4)| + 3, x = -0.9, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-2(-2|x + 2| + 1) - 1) - 3)/(-3(-2(-2|x + 2| + 1) - 1)) and g(x) = -2sin(3π(5x + 2) - 1) - 3 between the vertical lines x = -2.7 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 3.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3cos(1π(-1|((-3(1x^2) + 3)/(-1(1x^2) - 3)) + 3| + 2) - 2) + 2, g(x) = 2sin(1π((-2(5x^2 - 3x - 4) + 3)/(-3(5x^2 - 3x - 4) + 2)) + 3) + 1, x = 1.4, and x = 3.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\bo... | 6.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-1e^(-2(-2(-4x + 2)^2 - 4(-4x + 2) + 3)) + 2) - 1)/(3(-1e^(-2(-2(-4x + 2)^2 - 4(-4x + 2) + 3)) + 2) - 2), g(x) = (3(3(3|x - 2| - 1)^2 - 1(3|x - 2| - 1) - 5))/(2(3(3|x - 2| - 1)^2 - 1(3|x - 2| - 1) - 5) - 1), x = 1.2, and x = 2.8. Round y... | 3.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(-1((3x + 2)/(2x - 3))^2 - 1((3x + 2)/(2x - 3)) - 3) - 4, g(x) = -2(2cos(2πx + 3) + 2) - 5, x = -0.5, and x = -0.4. 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) = -2(-4(-3|((-2x)/(2x - 1)) + 2| + 2)^2 + 2(-3|((-2x)/(2x - 1)) + 2| + 2) + 3) + 1, g(x) = 1|((-1(-1x^2 + 4x + 4) + 3)/(-2(-1x^2 + 4x + 4) + 1)) - 1| + 2, x = 0.8, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaT... | 0.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(-4(3e^(1(-1x^2 + 3x - 4)) - 1) - 4) + 3| - 3, g(x) = 2sin(3π(-3(1x^2 + 4x - 3) + 4) + 1), 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": "user"
}
] | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1(3sin(2π((3x)/(-1x + 2)) + 1) - 1)^2 - 2 and g(x) = 2|(-2sin(2πx + 1) - 3) + 1| - 3 from x = 2.7 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3|(-1((3x - 2)/(3x - 2)) + 3) + 1| + 1)^2 - 4(-3|(-1((3x - 2)/(3x - 2)) + 3) + 1| + 1) + 2 and g(x) = 5(1|((-1x + 1)/(-3x + 2)) + 2| - 3) - 5 between the vertical lines x = 0.7 and x = 0.7999999999999999. Round to 1 decimal place... | 11.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(1e^(1((-3x - 2)/(2x + 2))) - 1) - 1, g(x) = -2(-3x)^2 + 3, x = -0.3, and x = 0.2. Round your answer 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) = -2sin(1π(4(5x^2 + 5) - 2) - 1) + 2 and g(x) = 1|(2sin(3πx + 2)) - 1| + 2 between the vertical lines x = 1.4 and x = 1.5. 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) = (-3(-3(5(-2|x + 3| + 2)^2 + 1(-2|x + 3| + 2)) - 1) - 1)/(2(-3(5(-2|x + 3| + 2)^2 + 1(-2|x + 3| + 2)) - 1) + 1) and g(x) = 2(-4((3x - 1)/(2x + 2)) + 1)^2 - 3(-4((3x - 1)/(2x + 2)) + 1) - 1 between the vertical lines x = 0.3 and x = 0... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(3(-2x + 2)^2 - 2) + 1| and g(x) = 3(1|x|) - 1 between the vertical lines x = 0.9 and x = 1.0. 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) = 3|((-2(-1x^2 + 2x + 2))/(-3(-1x^2 + 2x + 2) - 1)) - 3| - 3, g(x) = 1|(1e^(-1x) - 3) - 2| - 1, x = -2.3, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 4.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1cos(3π(-1|(2x + 2)| - 1) + 1) - 2 and g(x) = -3(3x^2 + 4x - 5) from x = -2.2 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(-3|((3(1e^(-2x) - 1) - 1)/(2(1e^(-2x) - 1) - 3)) - 2| + 3) - 5 and g(x) = -3|(3(-4x - 3)^2 - 2(-4x - 3) + 3)| - 1 from x = -0.5 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 94.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(-1((1x + 3)/(-3x)))^2 + 2(-1((1x + 3)/(-3x))) + 4, g(x) = 5(1x^2 + 3x + 2) - 2, x = -2.7, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-1(1|(3x - 5) - 3| - 3) + 1)/(-3(1|(3x - 5) - 3| - 3) + 1) and g(x) = 2(-3x - 2)^2 + 3(-3x - 2) 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"
}
] | 0.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(2|(1x - 1) - 3| - 2)^2 - 1(2|(1x - 1) - 3| - 2), g(x) = 3|(2sin(2πx - 2) - 2) + 2| - 1, x = 2.8, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(3(-3x + 5)^2 - 2(-3x + 5) + 1) + 1| - 1 and g(x) = (1(1cos(2πx + 1)) + 3)/(-2(1cos(2πx + 1)) - 1) from x = 0.5 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 4((-3(1|(4x^2 - 2x) - 2| + 2) + 1)/(-1(1|(4x^2 - 2x) - 2| + 2) - 2)) - 4, g(x) = (-2(2e^(-1(-4x^2 - 3x + 1)) - 3))/(-2(2e^(-1(-4x^2 - 3x + 1)) - 3) + 3), x = -1.2, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in L... | 6.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2sin(1π(3(3|((3x + 1)/(-1x - 3)) + 3| - 3)^2 - 1(3|((3x + 1)/(-1x - 3)) + 3| - 3))), g(x) = 2sin(1π((-1(1x + 5) + 1)/(-1(1x + 5) + 3)) - 1) + 2, x = -4.2, and x = -4.1000000000000005. Round your answer to 1 decimal place.\n\nPresent the answ... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1cos(1π(-3|((1(-2x^2 - 2x + 3) - 1)/(3(-2x^2 - 2x + 3) + 2)) + 3| + 2) + 3) + 1, g(x) = 4(-1|((1x + 1)/(3x - 2))| + 2) - 2, x = 0.3, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 45.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1sin(3π(-2|(-5x^2 + 1x + 2) + 3| + 2) - 2) - 2 and g(x) = 5((2x - 3)/(2x + 1))^2 + 1((2x - 3)/(2x + 1)) - 4 from x = 2.9 to x = 3.0. 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) = 1|(-3(5((1x + 1)/(-2x - 3))^2) + 2) - 3| + 2 and g(x) = -4(-2|(-3sin(1πx - 2) - 3) - 2| + 2) + 5 from x = -2.0 to x = -1.4. 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(-3|(4((2x)/(-2x))^2 + 5((2x)/(-2x)) + 3) + 1| + 3) + 2 and g(x) = 5((-3(3cos(3πx + 2)) + 2)/(-3(3cos(3πx + 2)) - 3)) - 2 from x = -1.2 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 19.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-1(5(2|x - 2| - 3) - 2) - 3)/(-2(5(2|x - 2| - 3) - 2)), g(x) = -5(1|x - 1| - 3)^2 + 2(1|x - 1| - 3) + 2, x = 3.5, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 7.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(2(2|(3cos(2πx - 1) - 1) + 2| - 2) - 3)^2 - 1(2(2|(3cos(2πx - 1) - 1) + 2| - 2) - 3) + 5 and g(x) = -5(-4(-2|x - 3| + 1)^2 + 4(-2|x - 3| + 1) + 5) - 5 from x = 3.0 to x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format... | 40.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1|(-3e^(1(-2x^2 - 5x + 2))) + 3| - 3) - 2 and g(x) = -3e^(-2(2(1|x| + 2)^2 + 4(1|x| + 2))) between the vertical lines x = 0.3 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1e^(-1((1(-3|(1x^2 + 5x + 4) + 2| + 1) + 2)/(3(-3|(1x^2 + 5x + 4) + 2| + 1) + 3))) and g(x) = -1|(-1(2cos(2πx + 2) - 2)^2 - 1) + 1| + 3 from x = -3.6 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your... | 1.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(3sin(3π(1|x + 1|) + 3) + 1) - 2, g(x) = -1(-3|x + 3| + 2)^2 + 4(-3|x + 3| + 2) + 4, x = -4.3, and x = -4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(-1|(3((2x)/(-1x + 3))^2 + 5((2x)/(-1x + 3)) + 1) - 1|) - 4 and g(x) = -2(1sin(1π(-2|x + 2| + 1) + 2) + 3)^2 + 5(1sin(1π(-2|x + 2| + 1) + 2) + 3) + 2 from x = -3.7 to x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format... | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-5(-2cos(2πx - 2) - 3) + 4) + 2)/(-3(-5(-2cos(2πx - 2) - 3) + 4)) and g(x) = (-1(-3sin(3πx - 3) + 1) + 3)/(-3(-3sin(3πx - 3) + 1) + 1) between the vertical lines x = 2.0 and x = 2.3. Round to 1 decimal place.\n\nPresent the answe... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1((-1(-4(-2|x - 3| + 2) - 5) + 2)/(2(-4(-2|x - 3| + 2) - 5) + 2))^2 - 4((-1(-4(-2|x - 3| + 2) - 5) + 2)/(2(-4(-2|x - 3| + 2) - 5) + 2)) + 1 and g(x) = -1((3(1cos(1πx - 3) + 2) + 1)/(2(1cos(1πx - 3) + 2) + 2))^2 - 4((3(1cos(1πx - 3) + 2) + 1... | 29.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3((1(-1|(2x^2 - 1x + 1) + 3|))/(1(-1|(2x^2 - 1x + 1) + 3|))) + 1, g(x) = 5(3|(4x^2 - 2x - 4)| - 3) + 1, 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": "u... | 1.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3|(-2x - 4)| - 1)^2 - 3(-3|(-2x - 4)| - 1) + 4 and g(x) = 3cos(1π(-4x^2 + 1x + 2) + 3) - 1 between the vertical lines x = -1.5 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3|((-2(4x^2 - 1x - 4))/(-2(4x^2 - 1x - 4) + 3)) - 1| - 2, g(x) = -5((-1x)/(3x + 1)) + 3, x = -0.2, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3(3cos(1π(-2|((-1x + 2)/(1x + 2))| + 2) - 3) + 3) - 4, g(x) = (-1(1|(2x^2 - 1x - 3) + 3|) - 3)/(2(1|(2x^2 - 1x - 3) + 3|) - 1), x = -2.6, and x = -2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your... | 0.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(3|((-3x - 2)/(3x)) - 1| - 3) + 4, g(x) = (-3(-3x - 2) - 3)/(3(-3x - 2) - 1), x = -0.7, and x = -0.4. 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) = 1(2|(-2x^2 - 2x - 4) + 2|) - 2 and g(x) = (3(-5x^2 - 4x) - 3)/(-2(-5x^2 - 4x)) between the vertical lines x = -0.6 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "us... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((-2(-2sin(1π(-1x^2 - 1x - 3)) + 3) + 2)/(1(-2sin(1π(-1x^2 - 1x - 3)) + 3) + 3)) + 2| + 1 and g(x) = (-3(2(5x - 2)^2 - 1) - 3)/(-2(2(5x - 2)^2 - 1)) between the vertical lines x = 0.3 and x = 0.5. Round to 1 decimal place.\n\nPre... | 0.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(3((1(3|x - 2| - 2) + 2)/(2(3|x - 2| - 2) + 2)) + 3)^2 - 3(3((1(3|x - 2| - 2) + 2)/(2(3|x - 2| - 2) + 2)) + 3) + 4 and g(x) = -3((1(-3sin(3πx) - 1))/(-1(-3sin(3πx) - 1) - 2)) between the vertical lines x = 0.0 and x = 0.3. Round t... | 26.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1|(3cos(1π(1x + 5) - 2) - 1) + 2| + 2, g(x) = 1|(3cos(1πx - 1) + 3) - 3|, x = -3.0, and x = -1.2. 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) = -5(-1(3cos(1πx - 2)) + 5)^2 and g(x) = (-2(-3cos(3πx + 2) - 2) - 3)/(3(-3cos(3πx + 2) - 2) - 2) between the vertical lines x = 2.2 and x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 20.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-1|(1x^2 + 3x - 2) - 2| + 3) - 4, g(x) = -1|(-3e^(-1x) - 3) + 3| - 1, x = 0.4, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1((-3(-3x^2 + 4x + 5))/(-2(-3x^2 + 4x + 5) - 1)) + 4, g(x) = -3sin(3π(1|x| - 1) + 1) + 3, x = -0.1, and x = 0.1. 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|((-3(-4x^2 + 2x + 4) + 1)/(1(-4x^2 + 2x + 4) + 3))| - 1, g(x) = -1cos(3π((3x + 3)/(3x + 1)) + 1) + 3, 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": "u... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1((3(1x^2 + 1x - 2) + 1)/(3(1x^2 + 1x - 2))) - 1, g(x) = -2cos(1π(1|x - 2| + 2) - 2) - 2, x = 0.8, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2((1(1|(-4x - 4) + 1| - 1) - 3)/(-3(1|(-4x - 4) + 1| - 1) + 4))^2 - 5((1(1|(-4x - 4) + 1| - 1) - 3)/(-3(1|(-4x - 4) + 1| - 1) + 4)) + 3 and g(x) = (3(3cos(1π(3x) + 2)) + 1)/(2(3cos(1π(3x) + 2)) + 3) from x = 0.7 to x = 0.9. Round to 1 decim... | 0.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3sin(1π((1(-5x + 5) + 1)/(2(-5x + 5) + 3)) - 1) + 1)| + 1 and g(x) = (2(-4(-1x)^2 + 2(-1x) + 5) - 2)/(3(-4(-1x)^2 + 2(-1x) + 5) + 2) between the vertical lines x = 1.0 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer... | 0.6 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(2(-5x - 2)^2 - 4(-5x - 2) + 1) + 2)/(2(2(-5x - 2)^2 - 4(-5x - 2) + 1) - 1), g(x) = (3(2x^2 - 1x - 5) + 3)/(-1(2x^2 - 1x - 5) + 2), x = -0.7, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxe... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(-3(-3|((-3x)/(-1x - 3)) + 3|)^2 + 1(-3|((-3x)/(-1x - 3)) + 3|)) + 4 and g(x) = -1(-2e^(-1(2|x + 3| - 3)) - 2) - 3 from x = -1.5 to x = -1.4. 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) = (-1(-1|(-2(-1e^(1x) + 3)^2 + 5(-1e^(1x) + 3) - 1) - 3| + 1) + 2)/(2(-1|(-2(-1e^(1x) + 3)^2 + 5(-1e^(1x) + 3) - 1) - 3| + 1) + 2) and g(x) = 4(1e^(-1(-2x^2 + 4x - 4)) + 1) - 3 from x = 0.0 to x = 0.9. Round to 1 decimal place.\n\nPresent the ... | 73.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|((-1(4(-4x^2 - 3x - 4) - 2) + 3)/(-3(4(-4x^2 - 3x - 4) - 2) + 1)) - 2| + 2, g(x) = (-1(2(-1|x| - 2)^2 + 5(-1|x| - 2)) + 2)/(-2(2(-1|x| - 2)^2 + 5(-1|x| - 2)) + 3), x = -0.8, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent th... | 4.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2((2(2|x + 3| + 1) - 3)/(-3(2|x + 3| + 1) - 3)) - 3, g(x) = -1cos(3π(1|x + 2| - 3) - 1) - 2, x = -3.2, and x = -3.0. 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) = -2cos(3π(-4(-2x^2 - 3x - 4) - 5) - 3) + 2 and g(x) = 3sin(1π(-4x^2 + 2x - 5) - 1) - 3 from x = 1.5 to x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2e^(1((-2(1|x + 2| - 1) - 1)/(3(1|x + 2| - 1) + 1))) + 3 and g(x) = -3((1x + 3)/(1x + 3)) + 1 from x = -2.6 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((-3(3|(-1x^2 - 2x - 1) + 3|) - 3)/(2(3|(-1x^2 - 2x - 1) + 3|))) + 4 and g(x) = -2(-1|(-1x - 2) + 2| - 2)^2 - 3(-1|(-1x - 2) + 2| - 2) - 4 between the vertical lines x = 0.7 and x = 0.8. Round to 1 decimal place.\n\nPresent the ans... | 19.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((2(5x - 2) + 3)/(-3(5x - 2) + 4)) + 3| + 1 and g(x) = 1|(2x + 4) - 3| - 3 between the vertical lines x = 0.8 and x = 1.0. 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|(-3(1sin(2π(-2x^2 - 4x - 5) + 1)) - 3) + 2| and g(x) = (-1(-2|(1e^(1x)) + 2|) + 3)/(-1(-2|(1e^(1x)) + 2|) + 2) between the vertical lines x = 4.3 and x = 4.3999999999999995. Round to 1 decimal place.\n\nPresent the answer in LaTex... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(1π((2(-2|(2x - 5) + 2| + 3) - 2)/(-3(-2|(2x - 5) + 2| + 3) - 3)) + 3) + 3 and g(x) = (-2(-5(-3|x - 1|) - 5) - 2)/(3(-5(-3|x - 1|) - 5) + 1) between the vertical lines x = 0.7 and x = 1.3. Round to 1 decimal place.\n\nPresent th... | 2.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(3|(2cos(1πx - 2) - 2) + 1| - 1)^2 - 1(3|(2cos(1πx - 2) - 2) + 1| - 1) + 2 and g(x) = 1e^(2(4x^2 - 1x - 4)) + 3 between the vertical lines x = 0.3 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxe... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(-1|(-2cos(3π(-5x - 1)) + 1)| + 2) + 1)/(2(-1|(-2cos(3π(-5x - 1)) + 1)| + 2) - 3), g(x) = 3(-3(1|x - 3| - 1)^2 - 4(1|x - 3| - 1) - 5) - 1, x = 1.1, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \... | 8.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(3(-3(-1e^(2x))^2 + 2(-1e^(2x)) + 1) + 2))/(-2(3(-3(-1e^(2x))^2 + 2(-1e^(2x)) + 1) + 2) + 3) and g(x) = 5(1sin(3π(-1|x + 2| + 3) + 2))^2 - 4(1sin(3π(-1|x + 2| + 3) + 2)) - 5 from x = -3.3 to x = -2.8. Round to 1 decimal place.\n\nPresent ... | 3.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|((1(-3x - 4) + 1)/(1(-3x - 4) - 2)) - 2| - 2 and g(x) = 3cos(3π(-1x^2 - 3x) + 2) - 2 between the vertical lines x = -5.0 and x = -4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(5(1|(-3x^2 + 2x + 5) - 3| + 3) - 5) + 2)/(-2(5(1|(-3x^2 + 2x + 5) - 3| + 3) - 5) - 2) and g(x) = 1(3|(-3x - 5) + 3| - 1)^2 - 5(3|(-3x - 5) + 3| - 1) + 4 between the vertical lines x = -0.5 and x = -0.1. Round to 1 decimal place.... | 1.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(1cos(1π(-1x^2 - 1) + 1) - 1) + 2, g(x) = 3(-3sin(3πx + 2) - 3) - 1, x = -0.4, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.1 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.