messages listlengths 1 1 | ground_truth stringlengths 3 8 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(4((-2(4x - 1))/(-1(4x - 1) + 2))^2 - 5((-2(4x - 1))/(-1(4x - 1) + 2)) + 2) + 3| and g(x) = -3(1|(-1x - 3) + 1| + 1)^2 + 3(1|(-1x - 3) + 1| + 1) - 3 from x = -1.3 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format... | 18.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(5(-3cos(2πx + 3) + 3)) - 2)/(1(5(-3cos(2πx + 3) + 3)) + 2) and g(x) = 5(-1x + 1)^2 + 4(-1x + 1) - 4 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"
}
] | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(1(1cos(3πx - 3) - 1)^2 + 1(1cos(3πx - 3) - 1) - 3) - 1 and g(x) = -1((-2x + 1)/(-2x))^2 - 5((-2x + 1)/(-2x)) - 1 from x = 0.1 to x = 0.2. 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) = 3|(-3((-2(-3x - 4) + 2)/(-3(-3x - 4) - 3))^2 - 2((-2(-3x - 4) + 2)/(-3(-3x - 4) - 3)) - 5)| + 1, g(x) = 5(1(-1sin(2πx) - 2)^2 - 5(-1sin(2πx) - 2) - 3) - 1, x = -0.8, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer i... | 6.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-1|(2((-3x + 1)/(-1x - 1)) + 2) - 2|)^2 + 2(-1|(2((-3x + 1)/(-1x - 1)) + 2) - 2|) - 4 and g(x) = -1|(1(2sin(2πx))^2 + 4(2sin(2πx)) - 2) - 2| + 3 between the vertical lines x = 0.0 and x = 0.2. Round to 1 decimal place.\n\nPresent ... | 0.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(1|(1e^(2x) - 3) + 3| - 1)^2 - 3(1|(1e^(2x) - 3) + 3| - 1) - 4 and g(x) = 2(-2sin(2πx - 2)) - 1 between the vertical lines x = -0.8 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 1.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((1(1x - 4) + 3)/(-2(1x - 4))) - 3| and g(x) = -1(3x^2 + 2x + 4) + 5 between the vertical lines x = 0.9 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 94.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (2(-4(3|(-2x^2 + 3x + 3) + 2| + 2) - 3))/(2(-4(3|(-2x^2 + 3x + 3) + 2| + 2) - 3)), g(x) = (2(-4(-3cos(1πx - 2) + 1)^2 - 4(-3cos(1πx - 2) + 1) + 3) + 1)/(-1(-4(-3cos(1πx - 2) + 1)^2 - 4(-3cos(1πx - 2) + 1) + 3) + 2), x = -3.6, and x = -3.2. R... | 1.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1((-2(1|(-1x^2 - 2x + 1) + 2| - 3) - 3)/(-1(1|(-1x^2 - 2x + 1) + 2| - 3) - 1)) - 1 and g(x) = 3|(-3e^(-1(2x - 2)) - 3) + 1| - 2 from x = 0.4 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 21.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (2(-3(3cos(2πx + 3) + 1)^2 + 3(3cos(2πx + 3) + 1) + 1) + 2)/(-2(-3(3cos(2πx + 3) + 1)^2 + 3(3cos(2πx + 3) + 1) + 1) - 3) and g(x) = (-3(-1x + 4))/(2(-1x + 4) + 2) from x = 0.2 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in La... | 0.0 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1|(-2((3(-3cos(3πx + 2) + 1) + 2)/(-3(-3cos(3πx + 2) + 1) + 2)) + 4) + 2| + 2, g(x) = -3sin(1π((1(-5x + 5) + 1)/(3(-5x + 5))) - 2), x = -2.1, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 19.8 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π(3|(-2x + 3) + 1| - 1)) - 1 and g(x) = -3(3sin(3πx - 1) + 1) + 3 between the vertical lines x = 2.4 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 2.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(1((2(1|x + 1| + 1) + 1)/(1(1|x + 1| + 1)))) - 3 and g(x) = (3(-2|x + 3| + 1) + 3)/(3(-2|x + 3| + 1) + 2) between the vertical lines x = -3.8 and x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 42.5 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4((-1(-1|x| - 2) - 3)/(-3(-1|x| - 2) - 1)) + 4, g(x) = 3cos(3π(1x - 4)) + 1, 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"
}
] | 1.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2sin(2π((-2(-1x^2 + 2x) + 2)/(-1(-1x^2 + 2x) + 3)) - 2) and g(x) = 5(2x^2 + 1x - 5) - 5 from x = -2.0 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 70.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3cos(3π(-1(-3|x + 3| - 3)^2 + 5(-3|x + 3| - 3) + 2) - 1) - 1 and g(x) = -1e^(-1(-3|x - 1| + 3)) - 2 from x = 2.0 to x = 2.1. 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(-1(3|x - 2| - 1) - 2) + 3)/(1(-1(3|x - 2| - 1) - 2) + 3), g(x) = -1((2x - 2)/(-1x + 3))^2 + 3((2x - 2)/(-1x + 3)) - 3, x = 1.7, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 5.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3cos(3π(-1(-1|x - 3| + 2) - 1) - 1) - 3)^2 - 4 and g(x) = 3((-1(2|x - 3|) + 3)/(2(2|x - 3|) + 2)) - 2 between the vertical lines x = -3.2 and x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1sin(1π(-1|(5x - 4) + 1| + 1) - 3) - 1 and g(x) = -2|(-3x - 4) - 2| - 1 from x = -2.0 to x = -1.9. 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) = (1(3(-3sin(1πx - 1) + 3)^2 - 5(-3sin(1πx - 1) + 3) + 5) + 3)/(-2(3(-3sin(1πx - 1) + 3)^2 - 5(-3sin(1πx - 1) + 3) + 5)) and g(x) = 3cos(1π((-3x + 2)/(2x + 1)) + 2) - 3 between the vertical lines x = -0.9 and x = -0.8. Round to 1 deci... | 0.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(3(-3x - 4)^2 + 1(-3x - 4) + 2) - 1| + 2 and g(x) = 3cos(1π((-1x - 3)/(1x + 1))) - 1 between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (3(5(2e^(-2x) - 1)^2 - 1(2e^(-2x) - 1) - 3) - 3)/(1(5(2e^(-2x) - 1)^2 - 1(2e^(-2x) - 1) - 3)), g(x) = -2|(5x^2 + 3x - 5) + 1| + 3, x = 0.0, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{You... | 11.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-3cos(2π(-1(-3|x + 3| - 1)^2 + 1(-3|x + 3| - 1) + 5) - 2) - 1) - 1)/(-1(-3cos(2π(-1(-3|x + 3| - 1)^2 + 1(-3|x + 3| - 1) + 5) - 2) - 1) - 1) and g(x) = -3|(1(1x - 5)^2 - 1(1x - 5)) + 3| + 2 between the vertical lines x = 3.9 and x... | 1.2 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-4((3x - 1)/(2x))^2 + 2((3x - 1)/(2x)) + 1) - 2 and g(x) = -2(-1sin(2πx + 1) - 2)^2 - 4(-1sin(2πx + 1) - 2) + 5 between the vertical lines x = 0.2 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\bo... | 5.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(2(-5x + 4)^2 - 5) + 2| - 1 and g(x) = 5(-2|x + 3| + 2) + 3 from x = 0.2 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((1(3cos(2πx) - 1) + 3)/(3(3cos(2πx) - 1))) + 3 and g(x) = -1|(1x^2 - 2x + 2) - 1| + 3 between the vertical lines x = -2.2 and x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 7.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2(-3sin(1π((-3(-1x^2 + 3x + 3) + 3)/(-2(-1x^2 + 3x + 3) + 3)) - 2) + 2) - 2 and g(x) = 2(-5(2|x| - 2) - 4)^2 + 1 from x = -0.4 to x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 1.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(1π(-2((-2(1|x - 3| + 2) + 3)/(-2(1|x - 3| + 2) - 2))^2 + 5((-2(1|x - 3| + 2) + 3)/(-2(1|x - 3| + 2) - 2)) + 4)) + 1 and g(x) = 1(-2cos(2π((-1x - 1)/(1x - 3)) + 3) - 1)^2 + 1 between the vertical lines x = 0.8 and x = 0.9. Round... | 0.0 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3|(2sin(2πx - 3) + 1) - 2|) + 5 and g(x) = (-1(-2x) - 3)/(-3(-2x) + 2) between the vertical lines x = -3.0 and x = -2.6. Round 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) = (-1(-2|(-3(-2x + 3)^2 - 2(-2x + 3) + 2) - 1| - 3) - 3)/(1(-2|(-3(-2x + 3)^2 - 2(-2x + 3) + 2) - 1| - 3)) and g(x) = -1cos(1π((3(1x - 3) + 1)/(1(1x - 3) + 1)) + 2) between the vertical lines x = 2.0 and x = 2.1. Round to 1 decimal pl... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(-3(-1(-3|x + 2| - 3)^2 + 3(-3|x + 2| - 3) + 2) - 5) - 3)/(2(-3(-1(-3|x + 2| - 3)^2 + 3(-3|x + 2| - 3) + 2) - 5) - 1) and g(x) = 1cos(2π(-1(-2x^2 - 4) + 5)) - 2 from x = -4.9 to x = -4.800000000000001. Round to 1 decimal place.\n\nPresent... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(1(2|x + 1| + 2)^2 - 2(2|x + 1| + 2)) - 3)/(-1(1(2|x + 1| + 2)^2 - 2(2|x + 1| + 2)) + 3) and g(x) = -1(-1x^2 - 1x - 3) - 4 between the vertical lines x = -1.0 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex f... | 0.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1(-1e^(2(-2|(5x + 3) + 3| + 3)) + 1)^2 + 3, g(x) = 1((-3(-2x^2 - 3x + 4) + 1)/(2(-2x^2 - 3x + 4) + 2)), x = -1.0, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 6.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -5(-2|(3sin(2π(-1x^2 + 5x + 5) - 1) - 3) + 2| - 1) - 2, g(x) = (-3(3|(-2sin(1πx + 3) + 3) - 1| - 3) + 3)/(2(3|(-2sin(1πx + 3) + 3) - 1| - 3) - 1), x = -4.8, and x = -2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex f... | 67.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1π(1(-1|x - 1| + 1) - 2) - 1) and g(x) = 1(-5x^2 + 3x + 3) + 3 between the vertical lines x = -1.1 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1sin(2π(-2(5x + 3)^2 - 4)) - 2 and g(x) = (1(-4x^2 - 3x + 1) + 3)/(-3(-4x^2 - 3x + 1) + 2) 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"
}
] | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5((-2(5x^2 - 1x + 5))/(-2(5x^2 - 1x + 5) + 3)) - 3 and g(x) = 2|(3e^(-2x) + 1) - 2| + 2 from x = 0.2 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0.7 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 3((-1(-3x^2 + 5x + 4) + 2)/(1(-3x^2 + 5x + 4) + 1)) + 3, g(x) = 1(-5x + 4)^2 - 4, x = 0.3, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1((3(-3|x + 2| + 1))/(-2(-3|x + 2| + 1) + 3))^2 + 3) - 5 and g(x) = (1(5(-1x + 3)^2 + 2))/(1(5(-1x + 3)^2 + 2) - 3) between the vertical lines x = 2.6 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: ... | 20.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3(1sin(1π(3(-2|x - 2|)^2 + 5(-2|x - 2|) + 3) + 2) - 3) and g(x) = 1(-2cos(3π(-4x) - 3) + 3)^2 - 1 from x = -2.5 to x = -2.4. Round 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) = (-1(1(5(2cos(3πx - 1) - 1))^2 - 2(5(2cos(3πx - 1) - 1)) + 2) + 1)/(1(1(5(2cos(3πx - 1) - 1))^2 - 2(5(2cos(3πx - 1) - 1)) + 2) + 3), g(x) = (1(3cos(3π(3|x + 2| - 1) + 1) + 1) - 1)/(-1(3cos(3π(3|x + 2| - 1) + 1) + 1) + 2), x = 2.7, and x = 2.8... | 0.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(3(2(-3|x + 1| - 3) - 5)^2 - 3(2(-3|x + 1| - 3) - 5) - 5) - 2)/(2(3(2(-3|x + 1| - 3) - 5)^2 - 3(2(-3|x + 1| - 3) - 5) - 5) - 1) and g(x) = 2((-2(3cos(1πx - 2) - 1) - 3)/(1(3cos(1πx - 2) - 1))) from x = 2.0 to x = 3.2. Round to 1 decimal p... | 27.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((-3(-1x - 3) - 2)/(-1(-1x - 3) + 3)) - 2| and g(x) = -3cos(2π(-1|x - 1| - 1) - 1) - 1 between the vertical lines x = 1.1 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"r... | 1.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(4(3|(1x - 2) - 1| - 3)^2 - 2(3|(1x - 2) - 1| - 3) - 3) - 1)/(3(4(3|(1x - 2) - 1| - 3)^2 - 2(3|(1x - 2) - 1| - 3) - 3) + 1) and g(x) = (-1(-1(2|x - 1| - 2)^2 + 1(2|x - 1| - 2) + 4) + 3)/(-3(-1(2|x - 1| - 2)^2 + 1(2|x - 1| - 2) + 4) + 1) f... | 5.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(5(1(-2|x + 3|) - 4)^2 - 3(1(-2|x + 3|) - 4) + 1) - 2)/(3(5(1(-2|x + 3|) - 4)^2 - 3(1(-2|x + 3|) - 4) + 1) + 1) and g(x) = 3|((1(4x) + 3)/(2(4x) + 3)) + 3| - 2 from x = -0.4 to x = -0.30000000000000004. Round to 1 decimal place.\n\nPresen... | 26.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -1|(-2sin(3π(3x + 2) - 1) + 2) - 2| - 3 and g(x) = -5(-2sin(1πx) + 3)^2 + 3(-2sin(1πx) + 3) + 2 from x = 2.3 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2sin(1π((-3(-2(-3|x - 3| - 2)^2 + 5(-3|x - 3| - 2) - 2) - 2)/(-1(-2(-3|x - 3| - 2)^2 + 5(-3|x - 3| - 2) - 2) + 2))) + 3 and g(x) = 2(-3|(-1cos(2πx) + 2)| + 3)^2 - 2(-3|(-1cos(2πx) + 2)| + 3) - 3 from x = 1.2 to x = 1.8. Round to 1 decimal pl... | 27.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2cos(2π(2((-1(1x^2 - 4x + 5))/(1(1x^2 - 4x + 5) + 2)) + 1)) + 1, g(x) = -3|(3((-1x - 2)/(-2x + 3))^2 + 3((-1x - 2)/(-2x + 3)) - 2) - 2| + 2, x = 0.7, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: ... | 0.1 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(2(-2(2sin(3πx - 1) - 2) + 2)^2 + 5(-2(2sin(3πx - 1) - 2) + 2) + 1) - 2)/(-2(2(-2(2sin(3πx - 1) - 2) + 2)^2 + 5(-2(2sin(3πx - 1) - 2) + 2) + 1) + 3) and g(x) = -1cos(2π(-2(1x - 2)^2 + 4(1x - 2) + 2) + 1) + 2 from x = -2.4 to x = -2.3. Rou... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(2|(3cos(1πx - 1) + 1) + 3| - 1)^2 - 1(2|(3cos(1πx - 1) + 1) + 3| - 1), g(x) = (2(-3x + 5) + 3)/(-1(-3x + 5) + 2), x = 1.1, and x = 1.2. Round your answer 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) = (-1(3e^(1(5x^2 + 5x + 2)) - 1) + 2)/(1(3e^(1(5x^2 + 5x + 2)) - 1)), g(x) = 3cos(2π(-2|x - 3| - 1) + 3) + 1, x = -3.6, and x = -3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 0.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(3π((3(-2|(3x - 5) + 1| - 1) - 3)/(3(-2|(3x - 5) + 1| - 1))) + 1) + 1 and g(x) = -1((1(1|x - 3| - 1) + 1)/(1(1|x - 3| - 1) + 1))^2 + 1((1(1|x - 3| - 1) + 1)/(1(1|x - 3| - 1) + 1)) between the vertical lines x = 1.4 and x = 2.0. ... | 1.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(3π((-3(-1x^2 - 1x - 4) + 2)/(-1(-1x^2 - 1x - 4) - 3)) + 1) + 1 and g(x) = -1((2x + 2)/(-1x - 3)) between the vertical lines x = -0.8 and x = -0.7000000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: ... | 0.1 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3|(4((2x + 2)/(3x - 2)) - 1) + 1| + 2, g(x) = -3sin(1π(-5x - 5) + 1) - 3, x = -3.3, and x = -3.2. 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) = -3(3e^(1(-4(3|x - 2| - 3) + 4)) + 3)^2 - 3(3e^(1(-4(3|x - 2| - 3) + 4)) + 3) + 5 and g(x) = (-1(1|(-1cos(1πx) + 2) - 1| + 1) - 2)/(-2(1|(-1cos(1πx) + 2) - 1| + 1) + 3) from x = -1.7 to x = -0.3. Round to 1 decimal place.\n\nPresent the answe... | 51.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 2|(2sin(3π((3(2x + 5) - 1)/(1(2x + 5))) + 2) + 3)| and g(x) = -1(-1e^(-1((2x + 2)/(-1x))) + 2) + 1 from x = -2.4 to x = -2.3. 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) = 4(-1|(-1x^2 + 3x + 4) + 3| + 1) + 3 and g(x) = (-1(-5x - 4) + 2)/(1(-5x - 4)) between the vertical lines x = -1.8 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 2.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3(1((-2(-1|x - 1| + 3) + 1)/(-3(-1|x - 1| + 3) - 3))^2 + 4((-2(-1|x - 1| + 3) + 1)/(-3(-1|x - 1| + 3) - 3)) - 1) + 2, g(x) = -3e^(-1(1(1|x + 1| + 1)^2 + 4(1|x + 1| + 1) + 5)), x = 1.5, and x = 4.8. Round your answer to 1 decimal place.\n\nP... | 17.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 3sin(2π(-1(1|x| + 2)^2 - 1(1|x| + 2) + 2) + 1) and g(x) = -4((2x - 3)/(3x + 3))^2 + 5((2x - 3)/(3x + 3)) - 1 from x = 1.9 to x = 2.0. 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) = -3sin(3π((2(-1x - 2) + 3)/(2(-1x - 2) + 2)) + 2) + 2 and g(x) = 1e^(-1((1x + 2)/(-2x + 3))) + 1 between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 0.2 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -2(1sin(1π(-3x - 2) + 1) - 1)^2 + 5(1sin(1π(-3x - 2) + 1) - 1) + 4 and g(x) = -2sin(2π(-5x^2 + 4x - 4) - 1) + 1 from x = -0.6 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 3.8 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3cos(1π(3|(4((-2x + 1)/(2x - 3)) - 2) + 2| - 2) - 2) + 3 and g(x) = (-1(-1e^(-2(4x - 2))))/(2(-1e^(-2(4x - 2))) - 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"... | 0.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1(5(-2|((2x - 2)/(1x - 2)) + 3|) + 2)^2 + 2(5(-2|((2x - 2)/(1x - 2)) + 3|) + 2) + 1 and g(x) = 3|(-1(3x^2 + 4x - 5) - 5) + 2| + 3 from x = 1.5 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 6.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-2sin(3π(-4x^2 + 3x - 4) - 1) + 3) - 2| - 1 and g(x) = (-1(3sin(1πx + 3) - 2) - 2)/(-1(3sin(1πx + 3) - 2) + 2) between the vertical lines x = 4.0 and x = 4.1. 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) = -1|(-1((2x - 2)/(3x - 2)) - 1)| + 1 and g(x) = -2((-1x + 2)/(-1x - 2))^2 - 5((-1x + 2)/(-1x - 2)) + 1 between the vertical lines x = -1.0 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 15.9 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (1(-1(1cos(3π(-3x^2 - 3x - 1) - 1) - 3) - 4) - 3)/(2(-1(1cos(3π(-3x^2 - 3x - 1) - 1) - 3) - 4)) and g(x) = -1((1(3|x|) + 2)/(2(3|x|) + 1)) + 3 from x = 2.5 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{... | 4.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -4(2sin(2π(5x) - 3) + 1)^2 - 2(2sin(2π(5x) - 3) + 1) + 2, g(x) = 5(1cos(2πx)), x = -3.5, and x = -3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = -3e^(-2(2|(-1((-3x - 3)/(-3x - 2))^2 + 1((-3x - 3)/(-3x - 2)) + 5) - 1| + 1)) + 2 and g(x) = 3|((-2(-3x^2 + 2x + 4) + 1)/(-3(-3x^2 + 2x + 4) - 2)) + 3| + 1 from x = -0.9 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex fo... | 22.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 4(3(1|x + 2| - 3)^2 + 4(1|x + 2| - 3) - 4) - 1 and g(x) = 2|(-2x^2 - 5x + 4) - 1| + 1 from x = -1.4 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 86.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 1sin(2π(-5(1x - 2)^2 + 3(1x - 2) - 4) + 2), g(x) = 1(-1x^2 - 1) + 5, x = -2.0, and x = -1.9. 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) = -1(-1|(-5x^2 + 4x - 2)|) - 5, g(x) = -2(-2cos(3πx - 3)) - 5, x = 0.4, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1.5 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(5(1x + 3)^2 + 1(1x + 3) - 3) - 1)/(-1(5(1x + 3)^2 + 1(1x + 3) - 3) + 2) and g(x) = -1(2x + 4)^2 - 2(2x + 4) + 2 between the vertical lines x = -4.1 and x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \... | 2.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -1((3(-1|(-1x + 5) + 1| + 2) + 1)/(3(-1|(-1x + 5) + 1| + 2) + 3))^2 + 2((3(-1|(-1x + 5) + 1| + 2) + 1)/(3(-1|(-1x + 5) + 1| + 2) + 3)) + 1, g(x) = -5(3(1e^(-1x) + 2) + 1)^2 + 2(3(1e^(-1x) + 2) + 1) - 3, x = 3.0, and x = 3.1. Round your answe... | -12.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2(2|(3x^2 - 3x - 1)| - 3) + 1, g(x) = -3(-3cos(2πx - 1) - 1)^2 - 3(-3cos(2πx - 1) - 1) - 2, x = -0.1, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(3π((2(-3|(-5x - 1)| + 3))/(-2(-3|(-5x - 1)| + 3) - 1))) - 1 and g(x) = -5(1|((-1x)/(-3x + 1)) - 3| - 2)^2 - 5(1|((-1x)/(-3x + 1)) - 3| - 2) + 1 between the vertical lines x = 0.4 and x = 0.5. Round to 1 decimal place.\n\nPresen... | 0.5 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(3(1sin(1πx - 3) - 1) - 3) - 2)/(1(3(1sin(1πx - 3) - 1) - 3) - 3) and g(x) = -2cos(2π(-5x^2 + 4x - 5) - 3) - 3 from x = 4.5 to x = 4.6. Round 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) = 4(-4(-2cos(1πx - 3) - 1)^2 - 3(-2cos(1πx - 3) - 1) - 4) - 3, g(x) = -5(1cos(1πx - 1) + 3)^2 - 4(1cos(1πx - 1) + 3) - 5, x = 3.4, and x = 4.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 53.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(-5((-2(2sin(1πx + 1)) + 3)/(3(2sin(1πx + 1)) - 1))^2 + 5((-2(2sin(1πx + 1)) + 3)/(3(2sin(1πx + 1)) - 1)) + 1) - 2, g(x) = (-2(3e^(-2(3x^2 - 4x + 5)) - 1) + 3)/(-2(3e^(-2(3x^2 - 4x + 5)) - 1) + 1), x = -0.2, and x = 0.6. Round your answer ... | 4.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-2(-3x - 5) - 2)/(-3(-3x - 5) + 1))^2 - 1((-2(-3x - 5) - 2)/(-3(-3x - 5) + 1)) - 1 and g(x) = (3(-5x + 5) - 1)/(-3(-5x + 5) - 1) between the vertical lines x = -1.4 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in ... | 5.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (3(-3|(2cos(3πx - 1) + 3) - 2| + 1))/(2(-3|(2cos(3πx - 1) + 3) - 2| + 1) - 1) and g(x) = -2e^(-1((3x + 1)/(1x - 3))) - 2 from x = -4.8 to x = -4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 0.9 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(2(5(3|x + 1| - 1) + 5)^2 - 1(5(3|x + 1| - 1) + 5) - 2) - 1)/(-2(2(5(3|x + 1| - 1) + 5)^2 - 1(5(3|x + 1| - 1) + 5) - 2) + 3) and g(x) = -4((-2(3sin(2πx - 2) - 3) + 2)/(-3(3sin(2πx - 2) - 3) + 4)) - 3 between the vertical lines x ... | 1.1 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(2|(1((2x - 1)/(2x + 2))^2) - 1| + 1) - 1 and g(x) = (2(-2|(2e^(2x) - 3) - 2| + 2) + 2)/(-1(-2|(2e^(2x) - 3) - 2| + 2) - 2) between the vertical lines x = 0.2 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex fo... | 8.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (-2(-1(3(1|x| - 2) + 2)^2 - 2(3(1|x| - 2) + 2) - 3) + 1)/(2(-1(3(1|x| - 2) + 2)^2 - 2(3(1|x| - 2) + 2) - 3) - 1), g(x) = -3cos(1π((-1(-3x - 2) + 3)/(-1(-3x - 2))) + 1) - 3, x = -0.6, and x = -0.5. Round your answer to 1 decimal place.\n\nPre... | 0.3 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2(2|((-1(-3x^2 - 5x + 1) + 2)/(-1(-3x^2 - 5x + 1) - 1)) + 1| + 3) + 3, g(x) = -3|((1(5x^2 + 5x - 3) - 3)/(-1(5x^2 + 5x - 3) - 1)) - 1| + 1, x = -1.4, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: ... | 24.4 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(2sin(2π(-2(3x + 3)^2 + 3(3x + 3) + 1) + 1) + 2) - 1)/(-3(2sin(2π(-2(3x + 3)^2 + 3(3x + 3) + 1) + 1) + 2) + 2) and g(x) = 1(1|((-2x)/(-3x + 1)) + 3| - 1)^2 - 5(1|((-2x)/(-3x + 1)) + 3| - 1) - 1 from x = -1.4 to x = -1.2999999999999998. Ro... | 0.9 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(2(3|(1x + 2) - 3| + 2)^2 - 2(3|(1x + 2) - 3| + 2) - 5) - 1)/(2(2(3|(1x + 2) - 3| + 2)^2 - 2(3|(1x + 2) - 3| + 2) - 5) - 1), g(x) = -1(1e^(-1(-3|x - 2| + 3)) - 1)^2 + 1(1e^(-1(-3|x - 2| + 3)) - 1) - 4, x = 0.9, and x = 1.1. Round your answ... | 1.0 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-3(-5(2|(3x^2 + 4x + 3) + 1| - 3) + 4) - 3)/(3(-5(2|(3x^2 + 4x + 3) + 1| - 3) + 4) + 1) and g(x) = -1e^(-2(-1|((2x + 2)/(2x + 3)) - 2|)) + 3 from x = -3.1 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed... | 1.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -3|((-2(-1x + 5) + 2)/(1(-1x + 5) + 1)) + 1| + 2, g(x) = -1cos(2π(-1x + 5) + 3) + 1, 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) = 1(5(-2|((1x - 1)/(2x - 1)) - 1| + 3) + 3)^2 + 5(5(-2|((1x - 1)/(2x - 1)) - 1| + 3) + 3) - 2 and g(x) = -3|(-4(-5x + 2)^2 - 2(-5x + 2)) + 3| + 2 between the vertical lines x = 0.4 and x = 0.5. Round to 1 decimal place.\n\nPresent the... | -1069.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5((1(3sin(3πx - 2) + 3))/(3(3sin(3πx - 2) + 3) - 1))^2 + 4((1(3sin(3πx - 2) + 3))/(3(3sin(3πx - 2) + 3) - 1)) - 3 and g(x) = 1(-3|x - 1| + 1) - 1 from x = 0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\box... | 42.6 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = (-2(2e^(1(3|(1x^2 - 4x + 4) - 2| - 1)) - 3) + 2)/(-3(2e^(1(3|(1x^2 - 4x + 4) - 2| - 1)) - 3) + 2) and g(x) = (2(-1(-3e^(-1x) - 3)))/(-2(-1(-3e^(-1x) - 3))) from x = 3.2 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex for... | 0.8 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 2|(3e^(-1((-2(1x - 4) - 2)/(-3(1x - 4) + 4))) + 3) + 1| + 2, g(x) = (3(-3(-2sin(1πx - 2) - 3) - 4) - 1)/(-2(-3(-2sin(1πx - 2) - 3) - 4) + 3), x = -2.2, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format... | 10.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = -2|((-2(-5x - 1) - 2)/(3(-5x - 1) + 3)) + 2|, g(x) = -1|(-5x + 4) - 1| + 1, x = -0.1, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2.7 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 5(-1e^(1(5((2x + 1)/(2x))^2 + 3((2x + 1)/(2x)) - 2)) + 3) - 1 and g(x) = -3(-3e^(-2((1x + 2)/(1x + 3))) + 2)^2 + 1(-3e^(-2((1x + 2)/(1x + 3))) + 2) + 3 from x = -2.4 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex forma... | 70.6 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1|((-2x - 3)/(1x))| + 1)^2 - 3(-1|((-2x - 3)/(1x))| + 1) + 4 and g(x) = (1(2|x|) - 1)/(-2(2|x|) + 3) between the vertical lines x = 0.8 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 9.3 | MATH |
[
{
"content": "Calculate the area enclosed between the functions f(x) = 1((-3(2x - 3) - 3)/(1(2x - 3) + 2))^2 and g(x) = (2(3sin(1πx - 1) - 1) - 1)/(3(3sin(1πx - 1) - 1) - 2) from x = 3.1 to x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8.2 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = 5(-2|(-1x - 4)|)^2 + 1(-2|(-1x - 4)|) - 1, g(x) = -2sin(3π(1x - 3) - 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"
}
] | 0.4 | MATH |
[
{
"content": "Find the area of the region bounded by the curves f(x) = (1(5(-2cos(3πx + 2) - 3) + 4))/(-3(5(-2cos(3πx + 2) - 3) + 4) - 1), g(x) = (2(3cos(3πx + 1) - 1) + 3)/(2(3cos(3πx + 1) - 1) + 1), x = -4.3, and x = -3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 1.7 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((3(2|x| + 2) + 3)/(3(2|x| + 2) - 1)) - 1 and g(x) = 1|(-3cos(2πx - 1) + 1) - 1| - 2 between the vertical lines x = -1.7 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 0.3 | MATH |
[
{
"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((1(1|(-1x - 1) + 3| + 1) - 3)/(2(1|(-1x - 1) + 3| + 1) + 3))^2 + 3((1(1|(-1x - 1) + 3| + 1) - 3)/(2(1|(-1x - 1) + 3| + 1) + 3)) - 2 and g(x) = (-3(2(-1x^2 - 5x) + 5) - 1)/(2(2(-1x^2 - 5x) + 5) + 1) between the vertical lines x = -... | 1.3 | MATH |
End of preview. Expand
in Data Studio
No dataset card yet
- Downloads last month
- 7