messages list | ground_truth string | dataset string |
|---|---|---|
[
{
"content": "At what integer value (rounded) do the functions f(x) = (1(-1(2(3|x + 2| + 2)^2 - 4(3|x + 2| + 2) - 4) + 5) + 1)/(-2(-1(2(3|x + 2| + 2)^2 - 4(3|x + 2| + 2) - 4) + 5) + 3) and g(x) = -2|(3cos(2π((-1x + 1)/(1x)) - 3) + 1) + 3| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex f... | -2 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 1|(3(3x^2 + 2)) + 1| - 3 and g(x) = 5(3x^2 - 3x - 4) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 1(2cos(2π((-2x + 2)/(1x + 2))) + 2)^2 + 2(2cos(2π((-2x + 2)/(1x + 2))) + 2) + 4 and g(x) = -1cos(2π(-3|x + 1| - 2) + 3) + 3 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 10 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -1(-1(2|((1x + 2)/(1x + 1)) - 2|) - 2)^2 - 3(-1(2|((1x + 2)/(1x + 1)) - 2|) - 2) - 1 and g(x) = -3e^(-2((3(-1x + 5))/(-3(-1x + 5) - 2))) + 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent t... | 2 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 5(-1|((2x + 1)/(2x - 1))| + 2) and g(x) = (3(-2e^(1x)) + 3)/(2(-2e^(1x)) - 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 3cos(2π((-2(-3x^2 + 4x - 4) - 3)/(3(-3x^2 + 4x - 4) + 1)) + 3) + 1 and g(x) = 4((1x)/(-1x + 2))^2 - 2((1x)/(-1x + 2)) - 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 3|(-1(5x^2 + 2x - 2) - 4) - 1| + 1 and g(x) = 4(-2sin(1πx + 2) - 1)^2 - 2(-2sin(1πx + 2) - 1) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 0 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (-3(2|(-5(-2x^2 + 3x - 4) + 4) - 1| + 2) + 3)/(2(2|(-5(-2x^2 + 3x - 4) + 4) - 1| + 2) + 3) and g(x) = 1(2|(-2e^(-2x) - 1) + 2| - 3) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the... | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 1(-1cos(3π((3x + 1)/(2x - 3)) - 2) + 2) - 3 and g(x) = -1sin(1π(5x^2 - 3) - 3) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -8 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -2x - 1 and g(x) = 2x^2 + 5x - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (3(-5(2cos(3πx) + 2)^2 - 3(2cos(3πx) + 2) - 4) + 2)/(1(-5(2cos(3πx) + 2)^2 - 3(2cos(3πx) + 2) - 4) + 1) and g(x) = 1|((2x - 3)/(-3x))| + 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the... | 0 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 5(1(1cos(3π(2|x + 2| - 3) + 3) + 1)^2 + 3(1cos(3π(2|x + 2| - 3) + 3) + 1) + 2) + 2 and g(x) = 2((-1(-2x + 3) - 2)/(-3(-2x + 3) - 1))^2 + 3((-1(-2x + 3) - 2)/(-3(-2x + 3) - 1)) + 5 in the interval [-10, 10]... | 1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 2|(1((-2(1x - 4) + 1)/(1(1x - 4) - 3))^2 + 2((-2(1x - 4) + 1)/(1(1x - 4) - 3)) - 3) - 3| and g(x) = (-3(-2|(-3x^2 - 3x + 5) + 3| - 2) + 2)/(-2(-2|(-3x^2 - 3x + 5) + 3| - 2) + 1) intersect in the interval [-10, 10].\n\n... | 21 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (2(-3(5(-2|x + 3| - 2))^2 + 4) - 1)/(1(-3(5(-2|x + 3| - 2))^2 + 4) + 2) and g(x) = 2(3(-1|x - 1| + 1)^2 - 3(-1|x - 1| + 1) - 4) - 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer... | -1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -2((-2(2|(5x^2 + 4x + 1) - 3|) - 2)/(3(2|(5x^2 + 4x + 1) - 3|) - 2)) - 4 and g(x) = 1|(3(-4x^2 + 5x - 5) + 3) - 1| + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 1|(2(-1x^2 + 5x - 5) - 5) - 2| - 1 and g(x) = 1e^(2(-1x - 3)) + 3 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 4((-1(-1|x - 3|) + 1)/(3(-1|x - 3|) + 2)) + 3 and g(x) = -3|(-2x - 2) - 2| + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (-2(-4(2|(-1(-1e^(1x) + 1)^2 - 4(-1e^(1x) + 1) - 5) + 1| - 1) + 4))/(1(-4(2|(-1(-1e^(1x) + 1)^2 - 4(-1e^(1x) + 1) - 5) + 1| - 1) + 4) + 1) and g(x) = 5((3(1|(2x^2 + 2) + 1| - 1) + 2)/(3(1|(2x^2 + 2) + 1| - 1))) + 3 intersect in the interval [... | 1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 3((-2(-4x^2 - 4x - 1))/(-2(-4x^2 - 4x - 1) - 3)) + 3 and g(x) = -5(2x - 1)^2 + 3(2x - 1) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (2(5(1x^2 - 5x + 1) - 4) + 3)/(-3(5(1x^2 - 5x + 1) - 4) + 2) and g(x) = 3|(-2sin(1πx + 1) + 2) + 2| - 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\... | 5 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1(-1|(2((1x)/(-2x - 1)) + 2) + 1| - 2)^2 + 5(-1|(2((1x)/(-2x - 1)) + 2) + 1| - 2) + 3 and g(x) = 2((2(-2|x - 2| - 1) + 1)/(2(-2|x - 2| - 1) + 2)) + 2 in the interval [-10, 10], rounded to the nearest inte... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-3(2|(3sin(2πx) + 2) + 3| + 2) + 1)/(-3(2|(3sin(2πx) + 2) + 3| + 2) + 1) and g(x) = -1(-1|x| - 2) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 3 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -5((2(-3|(-1x^2 - 4x - 1) - 3| + 2) - 1)/(-1(-3|(-1x^2 - 4x - 1) - 3| + 2) + 3)) - 1 and g(x) = 2e^(1(-2(4x - 4)^2 - 4(4x - 4) - 2)) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{You... | -1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 2|(1(4((-1x - 2)/(-2x + 3)) + 5)^2 + 2(4((-1x - 2)/(-2x + 3)) + 5) - 3) - 1| - 2 and g(x) = (-2(-2(1|x + 2| + 1)^2 + 5(1|x + 2| + 1)) + 3)/(1(-2(1|x + 2| + 1)^2 + 5(1|x + 2| + 1))) intersect in the interval [-10, 1... | -2 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1((-1(5(-2|x - 2| + 2)^2 - 3(-2|x - 2| + 2) - 4) - 1)/(2(5(-2|x - 2| + 2)^2 - 3(-2|x - 2| + 2) - 4) + 1)) - 1 and g(x) = -3|(-1((-2x - 1)/(-3x + 1)) + 1) - 3| intersect in the interval [-10, 10]?\n\nPresent the answer in ... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (2(-3e^(2(1(4x - 4)^2 - 1(4x - 4) - 3)) + 2) - 3)/(-3(-3e^(2(1(4x - 4)^2 - 1(4x - 4) - 3)) + 2) - 3) and g(x) = 2sin(2π(1|(-4x^2 - 1x + 5) + 1| + 3)) + 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?... | 4 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3(-1cos(2π((-3(2|x - 1| - 1) - 1)/(3(2|x - 1| - 1) - 2)) + 1) - 3) + 2 and g(x) = -3(-2|(-1x^2 - 2x + 3) - 3| + 3) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | -3 | MATH |
[
{
"content": "Find the third intersection point (counting from left to right) between the functions f(x) = 2(4((1(-2|x + 2| + 1) + 3)/(-1(-2|x + 2| + 1) + 2))^2 - 4((1(-2|x + 2| + 1) + 3)/(-1(-2|x + 2| + 1) + 2)) - 5) - 1 and g(x) = -3e^(-1((1(1x + 5) - 3)/(-2(1x + 5) - 1))) - 2 in the interval [-10, 10], round... | 2 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 3(-4((1(-3|x - 2| - 2) + 2)/(-2(-3|x - 2| - 2) + 3))^2 + 4((1(-3|x - 2| - 2) + 2)/(-2(-3|x - 2| - 2) + 3)) - 1) + 4 and g(x) = 1e^(1((2(4x^2) - 2)/(-2(4x^2) + 3))) - 3 meet in the interval [-10,... | 2 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 2(-3|((2x + 2)/(-3x - 2)) + 2| - 2) + 5 and g(x) = (2(4x^2 - 5x + 5) - 1)/(-1(4x^2 - 5x + 5) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your a... | -1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-1(-1|(-3e^(1(2x)) - 1) + 2| - 2) - 2)/(1(-1|(-3e^(1(2x)) - 1) + 2| - 2) - 3) and g(x) = -1|(3(-1e^(2x) - 1)^2 + 5(-1e^(2x) - 1) - 2) - 2| + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -2((-1(1x - 5) - 2)/(-1(1x - 5) + 3))^2 - 1((-1(1x - 5) - 2)/(-1(1x - 5) + 3)) - 2 and g(x) = -3e^(1(-5x + 4)) - 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format:... | 9 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -4x - 2 and g(x) = -4x^2 + 1x + 4 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 1e^(-1((-3(-3(4x + 2)^2 + 5(4x + 2) - 5) - 3)/(1(-3(4x + 2)^2 + 5(4x + 2) - 5)))) - 1 and g(x) = 3(2(3|x + 1| - 1)^2 - 4(3|x + 1| - 1) - 3) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent th... | -2 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (-3(1e^(-1(-1|(-5x^2 - 1x - 1) + 3| - 1)) + 2) + 1)/(-1(1e^(-1(-1|(-5x^2 - 1x - 1) + 3| - 1)) + 2) + 2) and g(x) = 5(-1|((-3x + 2)/(-1x - 1)) - 2| - 1)^2 + 1(-1|((-3x + 2)/(-1x - 1)) - 2| - 1) - 3 intersect in the interva... | 3 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(1(3|(1x - 3) + 1| - 1)^2 + 5(3|(1x - 3) + 1| - 1) - 1) - 3)/(-1(1(3|(1x - 3) + 1| - 1)^2 + 5(3|(1x - 3) + 1| - 1) - 1)) and g(x) = 3(2|(1x + 3)| - 2)^2 - 4(2|(1x + 3)| - 2) + 3 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the a... | 2 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1|(2((-2(4x - 5) - 1)/(-3(4x - 5)))^2 - 5((-2(4x - 5) - 1)/(-3(4x - 5))) + 5) - 1| + 3 and g(x) = 2(-3|((1x - 3)/(-2x - 3))| + 1)^2 + 4 meet in the interval [-10, 10]?\n\nPresent the answer in L... | 2 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1|(-4((-1(2x^2 + 2x) - 2)/(-2(2x^2 + 2x) - 3)) + 2) + 3| - 3 and g(x) = (-3(-5(3|x| - 3) - 2) - 2)/(2(-5(3|x| - 3) - 2) + 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex forma... | 0 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 1((-1(-3|x - 1| - 3) - 3)/(-1(-3|x - 1| - 3) + 2))^2 - 5((-1(-3|x - 1| - 3) - 3)/(-1(-3|x - 1| - 3) + 2)) + 1 and g(x) = (-3(-2x - 3) + 2)/(-1(-2x - 3) - 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Y... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2|(1((-3x - 1)/(2x)) + 3) - 3| - 2 and g(x) = 2((2x - 1)/(-1x + 2)) + 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -2(1sin(1π((1x - 1)/(2x - 1)) + 3) - 2) + 2 and g(x) = 3e^(-1(3x - 4)) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -5(-3|(5x - 4)| - 2)^2 - 3(-3|(5x - 4)| - 2) - 2 and g(x) = 5((-2x + 2)/(1x)) - 2 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1|(-3(4x - 5)^2 + 1(4x - 5) - 5) - 1| - 2 and g(x) = 1|((2x + 2)/(-1x - 1)) - 3| + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = 3((-1(-3e^(-2x) + 1) - 2)/(-3(-3e^(-2x) + 1) + 2)) and g(x) = -5((-1x - 2)/(-3x + 2))^2 + 4((-1x - 2)/(-3x + 2)) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2|((-2(-1x + 4) + 2)/(3(-1x + 4) - 1)) - 3| - 1 and g(x) = -5(1e^(-1x) + 2) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1(2((2(1|x + 1| - 2))/(2(1|x + 1| - 2) + 2))^2 + 1((2(1|x + 1| - 2))/(2(1|x + 1| - 2) + 2)) + 5) - 3 and g(x) = -1((3(-1|x - 1| + 2) - 2)/(2(-1|x - 1| + 2) - 1)) intersect in the interval [-10, 10].\n\nPresent the ... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -4(2|(1sin(2πx + 3) + 2) - 3| + 3)^2 - 3(2|(1sin(2πx + 3) + 2) - 3| + 3) - 4 and g(x) = -1|(-1e^(1x)) - 1| - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 5 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -4(-1((2(1|x + 1| - 3) + 3)/(-3(1|x + 1| - 3) + 1)) + 5)^2 + 5(-1((2(1|x + 1| - 3) + 3)/(-3(1|x + 1| - 3) + 1)) + 5) + 2 and g(x) = -5((3(-2x^2 + 4x) + 1)/(-1(-2x^2 + 4x) + 3)) + 2 intersect in the interval [-10, 10]?\n\n... | 2 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-1(2(1(1|x + 3| + 3)^2 - 2(1|x + 3| + 3) - 4) - 4) + 1)/(-1(2(1(1|x + 3| + 3)^2 - 2(1|x + 3| + 3) - 4) - 4) - 3) and g(x) = -2|((-3(-4x^2 + 2x) + 1)/(1(-4x^2 + 2x) - 3)) - 1| - 2 intersect in the interval [-10, 10... | -3 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-1(2sin(1π(2x^2 - 2x + 4) + 3) + 3))/(-1(2sin(1π(2x^2 - 2x + 4) + 3) + 3) - 2) and g(x) = 1|(-5x) - 3| - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | -1 | MATH |
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