messages listlengths 1 1 | ground_truth stringclasses 23 values | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -2((-2(2|x| - 3) + 1)/(1(2|x| - 3)))^2 + 2 and g(x) = (-1(2e^(1x)) - 1)/(2(2e^(1x)) - 1) intersect 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) = 1(-2|((3x + 3)/(2x + 3)) - 2| - 1) + 5 and g(x) = 2|((-2x + 1)/(3x + 3))| - 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | -2 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (3(-5(-1x + 3)^2 - 1(-1x + 3) + 3) + 2)/(3(-5(-1x + 3)^2 - 1(-1x + 3) + 3) - 2) and g(x) = (-2(2x^2 - 1x + 2))/(1(2x^2 - 1x + 2) - 3) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answ... | 6 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2((2(-1(2|x - 1| + 2)^2 + 5(2|x - 1| + 2) + 2) - 2)/(-1(-1(2|x - 1| + 2)^2 + 5(2|x - 1| + 2) + 2) - 3)) - 1 and g(x) = (2(4(3x + 1)^2 + 4(3x + 1) + 2) - 3)/(-2(4(3x + 1)^2 + 4(3x + 1) + 2) + 1)... | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-3(5(2|(4x + 2) - 2| - 2)^2 - 5(2|(4x + 2) - 2| - 2) - 4) - 3)/(-2(5(2|(4x + 2) - 2| - 2)^2 - 5(2|(4x + 2) - 2| - 2) - 4) - 2) and g(x) = 1|(5((-2x + 2)/(-2x - 2)) + 3) + 1| - 3 intersect in the interval [-10, 10]... | 0 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1(-1|((2(1x^2 - 4x + 2) + 1)/(3(1x^2 - 4x + 2) - 2)) - 3|) + 2 and g(x) = -4(3((-1x - 1)/(-1x)) + 1)^2 - 1(3((-1x - 1)/(-1x)) + 1) - 4 meet in the interval [-10, 10]?\n\nPresent the answer in La... | 4 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -1((1(1sin(1πx + 1)) - 3)/(1(1sin(1πx + 1)) - 3)) + 1 and g(x) = (-1(1|x - 1| - 2) + 2)/(1(1|x - 1| - 2) + 2) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\bo... | 2 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (-1(-3e^(-1(-2|x - 3| + 3)) + 2) + 3)/(2(-3e^(-1(-2|x - 3| + 3)) + 2) + 1) and g(x) = 1(1cos(3πx) - 1) - 4 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: ... | 2 | MATH |
[
{
"content": "Find the third intersection point (counting from left to right) between the functions f(x) = 1(4(3|((2x + 1)/(-2x + 3)) + 2|) + 2)^2 - 4(4(3|((2x + 1)/(-2x + 3)) + 2|) + 2) - 4 and g(x) = (-1(-5(2x + 5)^2 - 4(2x + 5) - 2) - 3)/(2(-5(2x + 5)^2 - 4(2x + 5) - 2) + 3) in the interval [-10, 10], rounde... | 4 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -3(-3|(2e^(1x) + 1) - 3| + 2) + 4 and g(x) = 2|(-2e^(1x) - 2) + 3| + 3 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) = -1sin(1π((2(4x^2 + 5x - 1))/(2(4x^2 + 5x - 1) - 1)) - 3) + 1 and g(x) = 1(1x^2 - 3x + 3) - 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your a... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-1(1(3(1e^(-1x) - 3) + 2)^2 + 3(3(1e^(-1x) - 3) + 2) - 3) + 2)/(1(1(3(1e^(-1x) - 3) + 2)^2 + 3(3(1e^(-1x) - 3) + 2) - 3)) and g(x) = 3e^(-1((-1(2|x + 1| - 1))/(-3(2|x + 1| - 1)))) + 2 meet in the interval [-10, 10].\n\nPr... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2(-1(2|((-2x - 2)/(2x + 2)) - 1| - 3) - 1)^2 + 4(-1(2|((-2x - 2)/(2x + 2)) - 1| - 3) - 1) - 5 and g(x) = -4(1e^(1(3x - 3)))^2 + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your a... | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -3(2|(-1((1x + 1)/(3x))^2 - 5((1x + 1)/(3x)) - 3)| - 1) - 5 and g(x) = -2(-2|(1cos(2πx - 1) - 3) - 3|)^2 - 3(-2|(1cos(2πx - 1) - 3) - 3|) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: ... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (1(2(3|(-1e^(-2x) - 3) - 1|)^2 + 1(3|(-1e^(-2x) - 3) - 1|) - 1) - 1)/(-1(2(3|(-1e^(-2x) - 3) - 1|)^2 + 1(3|(-1e^(-2x) - 3) - 1|) - 1)) and g(x) = 2(-3((-1x)/(-3x + 1)))^2 + 4(-3((-1x)/(-3x + 1))) - 1 meet in the interval [-... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1((1(5(1|x| + 2) + 4) - 1)/(2(5(1|x| + 2) + 4) + 1))^2 + 3((1(5(1|x| + 2) + 4) - 1)/(2(5(1|x| + 2) + 4) + 1)) - 4 and g(x) = 1(1e^(-1((3x - 2)/(2x - 1))) - 3) - 4 meet in the interval [-10, 10]?\n\nPresent the answer... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2((-1(-3|(-5x^2 - 4x - 3) - 3| - 3) + 2)/(-1(-3|(-5x^2 - 4x - 3) - 3| - 3) - 3)) - 1 and g(x) = 2|((-3(-5x - 2) + 2)/(-2(-5x - 2) + 3))| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\b... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -4((3(2|(1x - 4) + 1| + 2))/(3(2|(1x - 4) + 1| + 2) + 1))^2 + 5((3(2|(1x - 4) + 1| + 2))/(3(2|(1x - 4) + 1| + 2) + 1)) - 5 and g(x) = -1((-1(-3|x - 3| + 3) - 3)/(-2(-3|x - 3| + 3))) + 3 meet in the interval [-10, 10].\n\nPr... | 4 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -5(1|(-1e^(-2((-3x + 1)/(-3x + 4))) + 1) - 1|)^2 - 3(1|(-1e^(-2((-3x + 1)/(-3x + 4))) + 1) - 1|) + 4 and g(x) = -4(-3cos(1π(-3|x| + 3)) + 3) - 4 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPrese... | 1 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 2|(-1sin(3π(4x - 3) - 3) + 3) + 3| - 3 and g(x) = (-1(-1x^2 - 3x + 4) + 3)/(-1(-1x^2 - 3x + 4) - 1) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed... | -4 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1cos(3π(-2((-1x)/(-1x + 3))^2 - 2((-1x)/(-1x + 3)) - 5) - 2) - 1 and g(x) = 4(5x - 5)^2 - 4(5x - 5) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 1 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = -5(1|((-1x + 1)/(-3x + 2))| - 3) + 3 and g(x) = -1cos(1π((-2x + 3)/(-2x - 3)) - 3) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 5((-3(-3|x|) + 1)/(2(-3|x|) - 1)) and g(x) = -5((-1x - 3)/(2x))^2 - 3((-1x - 3)/(2x)) - 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\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) = -3|((-2(-3(3x^2 + 3x) - 5) - 1)/(-2(-3(3x^2 + 3x) - 5) + 3)) - 3| - 3 and g(x) = -1|(-4(2x^2 - 2x + 1) - 2)| meet 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 x-coordinate where the graphs of f(x) = -2(1|(-1(-3e^(-1x) + 2) - 4) - 3|)^2 + 1(1|(-1(-3e^(-1x) + 2) - 4) - 3|) + 4 and g(x) = -2e^(-1(-2((-1x - 3)/(-2x - 3)) + 4)) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your an... | -1 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 1e^(-1((3(3(-2|x + 3| - 2) - 2) + 1)/(1(3(-2|x + 3| - 2) - 2) + 2))) - 3 and g(x) = -1(3|(1x + 3) + 1| + 3)^2 + 5(3|(1x + 3) + 1| + 3) + 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the... | -8 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (-2(3(3|(5x) + 2| + 1)^2 - 5(3|(5x) + 2| + 1) + 2) + 1)/(-1(3(3|(5x) + 2| + 1)^2 - 5(3|(5x) + 2| + 1) + 2) + 2) and g(x) = 3((-2(-3|x| + 3))/(-2(-3|x| + 3)))^2 + 2((-2(-3|x| + 3))/(-2(-3|x... | 0 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (2(3(-2|(-4x^2 - 2x - 3) - 3| + 2) + 5) + 2)/(-3(3(-2|(-4x^2 - 2x - 3) - 3| + 2) + 5) - 1) and g(x) = 1(-3|((3x - 2)/(-1x + 3)) - 1| - 1) + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: ... | 2 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 2|((1(-3x^2 - 2))/(2(-3x^2 - 2) + 1)) - 2| - 1 and g(x) = (1(-2|x| + 2) + 3)/(-2(-2|x| + 2) + 1) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Y... | 1 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 2|(-1e^(-2((1x + 1)/(1x + 2))) - 3)| and g(x) = 3|(-4x^2 + 1x - 4) - 1| - 2 intersect in the range -10 ≤ x ≤ 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) = (1(4(-1|x - 1| + 3) + 4) - 2)/(3(4(-1|x - 1| + 3) + 4) - 2) and g(x) = 3(3cos(1πx + 2) + 3)^2 - 5(3cos(1πx + 2) + 3) + 4 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex f... | 2 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 2|(-4(-2((-1x - 2)/(-1x - 1))^2 + 5((-1x - 2)/(-1x - 1)) - 3) + 1)| and g(x) = 2|(-5(-1x^2 - 1x + 2) + 3) + 2| - 2 intersect 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) = 3(-2|((-3(3x^2 - 2x + 1))/(-2(3x^2 - 2x + 1) + 1)) + 1| - 1) + 1 and g(x) = (2(1|(2x - 3) - 1| - 2) + 3)/(3(1|(2x - 3) - 1| - 2) + 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 3 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -3|((-1(-3sin(2π(-5x^2 - 3x - 1) + 3) + 2) - 2)/(3(-3sin(2π(-5x^2 - 3x - 1) + 3) + 2))) - 1| - 2 and g(x) = -3e^(2(-3((2x - 2)/(-1x - 2)) + 5)) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answe... | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = -1((1(-2|x| - 3) + 1)/(-2(-2|x| - 3) - 3))^2 - 2((1(-2|x| - 3) + 1)/(-2(-2|x| - 3) - 3)) + 2 and g(x) = (-2(-1x - 5) + 3)/(-3(-1x - 5) + 1) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answe... | -5 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -1cos(1π(1|((1(2x^2 + 3x + 5) - 3)/(3(2x^2 + 3x + 5) + 2)) - 1| - 2) - 2) - 1 and g(x) = (1(5(2|x + 1|)^2 - 5) - 3)/(3(5(2|x + 1|)^2 - 5) + 2) in the interval [-10, 10], rounded to the nearest integer.\n\n... | -2 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 2((3(-5x + 1) - 2)/(3(-5x + 1) - 2))^2 - 4((3(-5x + 1) - 2)/(3(-5x + 1) - 2)) and g(x) = -1|((-3x + 3)/(1x - 3)) - 3| meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex form... | 4 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1|((-1(5x + 4) + 3)/(3(5x + 4) + 3))| + 3 and g(x) = (-3(1|x - 3| - 3) - 3)/(1(1|x - 3| - 3) + 3) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{... | 4 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 5((2(-3|x| - 1) + 1)/(-1(-3|x| - 1) + 3)) + 1 and g(x) = -1|(1e^(-1x) - 3) + 1| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -3(-5((3(-2|x - 2| - 3) + 2)/(-3(-2|x - 2| - 3)))^2 - 4((3(-2|x - 2| - 3) + 2)/(-3(-2|x - 2| - 3)))) - 2 and g(x) = -2|((1(3x^2 + 4x - 2) - 3)/(-1(3x^2 + 4x - 2))) - 3| intersect in the interval [-10, 10].\n\nPrese... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1(3sin(2π((3(2|x + 3|))/(2(2|x + 3|) + 3)) - 1) - 3)^2 + 2(3sin(2π((3(2|x + 3|))/(2(2|x + 3|) + 3)) - 1) - 3) + 2 and g(x) = 3|(-3e^(2(-4x - 5)) - 1) + 3| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTe... | -1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -2e^(-1((-1(-2(2x - 4)^2 - 2(2x - 4) - 2) - 2)/(-2(-2(2x - 4)^2 - 2(2x - 4) - 2) - 2))) - 1 and g(x) = (-1(5(2x^2 - 4x) - 2) - 1)/(-1(5(2x^2 - 4x) - 2) + 2) intersect in the interval [-10, 10].\n\nPresent the answer in... | 2 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 4((2(-4(-2|x + 2| - 2)^2 + 4(-2|x + 2| - 2) - 4) - 2)/(-2(-4(-2|x + 2| - 2)^2 + 4(-2|x + 2| - 2) - 4) + 3)) and g(x) = 2((-2(2x^2 + 3x - 3))/(-1(2x^2 + 3x - 3) - 3)) meet in the interval [-10, 1... | -1 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (1(-5(1e^(-1(3x^2 - 5x + 1)) + 1)) - 2)/(-1(-5(1e^(-1(3x^2 - 5x + 1)) + 1)) - 1) and g(x) = -4(-2e^(1((2x + 3)/(-2x - 2))) + 2) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | -1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -5(-3(-1|((-1x + 2)/(-1x + 2)) - 1| + 2) - 2)^2 - 3(-3(-1|((-1x + 2)/(-1x + 2)) - 1| + 2) - 2) - 2 and g(x) = -5(3(-3|x + 1| + 3)^2 - 3(-3|x + 1| + 3) - 4) + 4 intersect in the interval [-10, 10].\n\nPresent the an... | -1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1|((-3(5(-3x^2 + 3x + 3) - 1) + 2)/(3(5(-3x^2 + 3x + 3) - 1) + 2)) + 3| - 3 and g(x) = (-3(1(-2|x - 1| - 2)^2 + 1(-2|x - 1| - 2) - 5) + 1)/(-1(1(-2|x - 1| - 2)^2 + 1(-2|x - 1| - 2) - 5) + 3) me... | 1 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -1|(1sin(1π(1((2x - 2)/(-2x + 1)) - 2)) - 1) + 1| - 3 and g(x) = (-1(1(2x^2 - 4x - 2) - 5))/(-1(1(2x^2 - 4x - 2) - 5) - 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your an... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2(-3(-3|((-3x - 1)/(1x - 2)) - 2| + 1) + 3)^2 + 1(-3(-3|((-3x - 1)/(1x - 2)) - 2| + 1) + 3) + 5 and g(x) = 3|((2(2cos(1πx + 1) - 2) + 1)/(-3(2cos(1πx + 1) - 2) + 2)) - 2| + 1 intersect in the interval [-10, 10]?\n\nPrese... | 1 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2((-2(-1x - 5) + 3)/(1(-1x - 5) + 3))^2 - 5((-2(-1x - 5) + 3)/(1(-1x - 5) + 3)) - 1 and g(x) = -3sin(1π((-3x - 1)/(1x + 3)) - 2) + 1 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent ... | -7 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 5((-2(-2cos(2πx + 3) + 3) - 2)/(-3(-2cos(2πx + 3) + 3) + 4))^2 + 5((-2(-2cos(2πx + 3) + 3) - 2)/(-3(-2cos(2πx + 3) + 3) + 4)) + 3 and g(x) = -5((1x + 3)/(3x + 3)) - 4 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex... | -1 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2|((3(1x - 2) - 2)/(-2(1x - 2)))| + 2 and g(x) = 3(-3|x - 2| - 1)^2 - 1(-3|x - 2| - 1) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -4(2|(-1x - 5) + 2| - 3)^2 + 1(2|(-1x - 5) + 2| - 3) - 1 and g(x) = (-1(3|x| + 2) + 3)/(-1(3|x| + 2) + 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 0 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-1(-2e^(1(-1(-1x + 3)^2 + 3(-1x + 3))) + 2) - 2)/(1(-2e^(1(-1(-1x + 3)^2 + 3(-1x + 3))) + 2) + 3) and g(x) = 2|(-4(4x^2 + 4x - 4) - 3) - 1| - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex f... | -1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-3(-1(-1|(3x - 1) - 2|)^2 - 1(-1|(3x - 1) - 2|) + 3) - 1)/(-2(-1(-1|(3x - 1) - 2|)^2 - 1(-1|(3x - 1) - 2|) + 3) + 3) and g(x) = 2e^(1(-4(-1x^2 - 3x) + 4)) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex... | -3 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -1((3(-1|(-1x + 5) - 3| - 2) - 2)/(2(-1|(-1x + 5) - 3| - 2) + 2))^2 + 3((3(-1|(-1x + 5) - 3| - 2) - 2)/(2(-1|(-1x + 5) - 3| - 2) + 2)) - 2 and g(x) = 1|((-1(2x^2 - 3x - 1))/(1(2x^2 - 3x - 1) - 2)) - 1| - ... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 4((-2(-1|(-1x^2 + 3x - 2)| + 1))/(2(-1|(-1x^2 + 3x - 2)| + 1) - 1)) - 2 and g(x) = (-1(-2e^(-1(1x)) - 2))/(2(-2e^(-1(1x)) - 2)) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in ... | 3 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3|(2sin(1π((-1(2x - 4) + 1)/(1(2x - 4))) + 2) - 2) - 2| - 3 and g(x) = -3(5(1e^(2x) - 3) + 5)^2 - 1(5(1e^(2x) - 3) + 5) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 0 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1sin(2π(1|(-1x + 2) + 3| + 3) - 1) + 3 and g(x) = -1((-2x)/(3x + 2))^2 + 5((-2x)/(3x + 2)) - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | -1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -4(-4(1|((3x - 3)/(-2x + 1)) - 1|) - 1)^2 - 5 and g(x) = (-3(-3(-2|x - 2| - 1) - 5) + 3)/(-1(-3(-2|x - 2| - 1) - 5) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTe... | 3 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (2(4(4(-2|x - 3| - 2)^2 + 3(-2|x - 3| - 2) - 5) + 4))/(2(4(4(-2|x - 3| - 2)^2 + 3(-2|x - 3| - 2) - 5) + 4) - 1) and g(x) = 3(-2|((1x - 1)/(2x - 1)) - 3| + 3) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer... | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 4((-2(1cos(3πx + 1) + 3) + 3)/(2(1cos(3πx + 1) + 3)))^2 + 3((-2(1cos(3πx + 1) + 3) + 3)/(2(1cos(3πx + 1) + 3))) and g(x) = (1(-4x) - 3)/(2(-4x) - 1) intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Y... | 0 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -3(4((2x - 2)/(-3x + 2))^2 - 5((2x - 2)/(-3x + 2)) - 1) + 4 and g(x) = (-3(-1x^2 + 3x - 2) + 2)/(1(-1x^2 + 3x - 2)) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 3 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 2e^(-2(-2|((3(-5x + 3) - 1)/(-3(-5x + 3) + 4))| - 1)) + 3 and g(x) = -3(-2|(3x^2 - 3x + 2) - 1|) + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1(3|(-2e^(-1(-4x^2 + 1x + 4)) - 2) + 3| + 2) + 2 and g(x) = -2((-3(-1|x + 1| + 1))/(-1(-1|x + 1| + 1) - 2)) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 1 | MATH |
[
{
"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (1(-5(-2|(2sin(1πx + 3) + 2) + 1|)^2 - 1(-2|(2sin(1πx + 3) + 2) + 1|)) - 3)/(-1(-5(-2|(2sin(1πx + 3) + 2) + 1|)^2 - 1(-2|(2sin(1πx + 3) + 2) + 1|)) - 3) and g(x) = (1(5(-1x + 4)^2 - 4(-1x... | 4 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1(1|((2(-3x^2 - 2x + 3) - 2)/(-3(-3x^2 - 2x + 3))) - 1| + 3) + 1 and g(x) = (2(1|(3x - 5) - 1|))/(1(1|(3x - 5) - 1|) - 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: ... | 2 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = (1(-2(-1|(-3x + 4) - 2| + 3)^2 + 4(-1|(-3x + 4) - 2| + 3) + 4) - 2)/(-2(-2(-1|(-3x + 4) - 2| + 3)^2 + 4(-1|(-3x + 4) - 2| + 3) + 4) + 3) and g(x) = -1(-2|(4x + 5) - 1| - 2)^2 - 1(-2|(4x + 5) - 1| - 2) + 2 meet in the interval [-10, 10]... | -2 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -2cos(2π((-2(-5(-1|x - 2|) + 4))/(-2(-5(-1|x - 2|) + 4) + 3)) + 1) + 2 and g(x) = 3(1e^(2((-2x)/(-2x - 3))))^2 - 4(1e^(2((-2x)/(-2x - 3)))) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 2|(-1(1((-2x + 3)/(-1x + 3))^2 - 1((-2x + 3)/(-1x + 3)) + 2) + 2) - 3| - 1 and g(x) = (3(2|(-1x^2 + 5x - 4) + 3| + 1) + 3)/(3(2|(-1x^2 + 5x - 4) + 3| + 1) - 2) meet in the interval [-10, 10]?\n\... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 3e^(-2(-2|((2(1x^2 - 4x - 2) + 2)/(2(1x^2 - 4x - 2) + 3)) - 1| + 2)) and g(x) = (-2(-3(-5x + 3)^2 + 1(-5x + 3)) - 1)/(3(-3(-5x + 3)^2 + 1(-5x + 3)) - 2) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format... | 0 | MATH |
[
{
"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1(-3|(1(-2e^(-1x) + 3)^2 - 4(-2e^(-1x) + 3) - 2) + 1| + 3) - 4 and g(x) = -3sin(3π((2(-2x - 4) - 3)/(-2(-2x - 4))) - 2) - 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer... | 0 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = 3|((2(1x - 5) + 2)/(-3(1x - 5) + 2)) + 2| - 3 and g(x) = (-3(2e^(-1x) - 3) + 1)/(2(2e^(-1x) - 3) - 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 2|(4(-5x + 5)^2 + 3(-5x + 5) + 2) + 3| - 2 and g(x) = 3|(-3sin(2πx - 2) - 3) - 3| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 1 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 2(-2sin(1π(1|((1x - 2)/(1x - 2))| + 3))) + 2 and g(x) = (-1(1|(2x^2 + 2x + 1) - 3| - 2) + 1)/(2(1|(2x^2 + 2x + 1) - 3| - 2) - 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | -2 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1(-4(2|((-2x + 1)/(3x + 1)) - 1| - 1)^2 - 3(2|((-2x + 1)/(3x + 1)) - 1| - 1) + 4) - 4 and g(x) = 2sin(3π(1|(2x^2 - 5x) + 2|) - 1) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Yo... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = 4((-1(-3|x - 2|) + 2)/(2(-3|x - 2|) + 2)) + 1 and g(x) = 1|(-1sin(1πx) + 3) - 3| - 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 1|(-2e^(2(-3((-1x + 1)/(2x - 3)) + 3)) + 3) + 1| + 3 and g(x) = 1|(1(1sin(3πx - 1) + 3)^2 - 5(1sin(3πx - 1) + 3) - 2) + 3| + 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in L... | 3 | MATH |
[
{
"content": "Find the integer closest to the largest x-value where the functions f(x) = (3(-1(5(-2e^(-1x) - 1)^2 - 4(-2e^(-1x) - 1) - 5) - 2))/(-2(-1(5(-2e^(-1x) - 1)^2 - 4(-2e^(-1x) - 1) - 5) - 2)) and g(x) = (2(1|(2x + 1)| - 3) - 1)/(-3(1|(2x + 1)| - 3) + 4) meet in the interval [-10, 10].\n\nPresent the ans... | 2 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (-2(4(3(-2|x|)^2 - 2) + 1) + 3)/(-2(4(3(-2|x|)^2 - 2) + 1) - 2) and g(x) = (2(-3|(3x - 1) - 3| - 2) - 3)/(1(-3|(3x - 1) - 3| - 2) - 2) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent ... | 0 | MATH |
[
{
"content": "Find the integer value closest to the x-coordinate where f(x) = 4(3((-3(-2|x - 2| + 1) - 1)/(2(-2|x - 2| + 1) + 1))^2 + 5((-3(-2|x - 2| + 1) - 1)/(2(-2|x - 2| + 1) + 1)) + 2) + 3 and g(x) = (-1(3(4x^2 - 3x - 4) + 1) + 1)/(-2(3(4x^2 - 3x - 4) + 1) + 3) intersect in the range -10 ≤ x ≤ 10.\n\nPresen... | 1 | MATH |
[
{
"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1(-3|((-3x - 1)/(-2x - 1))| + 1)^2 - 3(-3|((-3x - 1)/(-2x - 1))| + 1) + 4 and g(x) = (3(3x - 5) + 3)/(-2(3x - 5) + 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 2 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1|((-2(1(-1e^(-2x) + 1)^2 - 5(-1e^(-2x) + 1) + 1) + 3)/(3(1(-1e^(-2x) + 1)^2 - 5(-1e^(-2x) + 1) + 1) - 2))| and g(x) = 3|((3(-1sin(1πx + 3) - 1) + 3)/(-1(-1sin(1πx + 3) - 1) + 2)) - 3| + 2 intersect in the interval [-1... | 0 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 1(2((-3x + 3)/(-1x - 3))^2 - 1((-3x + 3)/(-1x - 3))) - 5 and g(x) = (1(5x^2 + 1x + 2))/(2(5x^2 + 1x + 2) + 1) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\bo... | 8 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = (2(-3(5(1|x - 2| - 1)^2 + 4) - 5) - 2)/(-2(-3(5(1|x - 2| - 1)^2 + 4) - 5) + 1) and g(x) = -2|((2(2x + 4))/(-1(2x + 4) - 2)) + 3| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | -4 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -4((-2(1|(-2x + 5) + 1|) - 1)/(-1(1|(-2x + 5) + 1|) + 3))^2 - 3((-2(1|(-2x + 5) + 1|) - 1)/(-1(1|(-2x + 5) + 1|) + 3)) + 3 and g(x) = (1(-1(3cos(3πx) + 3)^2 - 4(3cos(3πx) + 3) - 1) + 2)/(2(-1(3c... | 3 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = -2((3(2|x + 2| - 2) - 3)/(1(2|x + 2| - 2) - 2)) - 4 and g(x) = (3(3x - 5) - 3)/(-1(3x - 5) - 3) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answe... | -4 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -2cos(2π(-2|((-2x + 3)/(-2x + 1)) + 1| + 3) - 3) - 1 and g(x) = 1(3|x + 3|)^2 - 3(3|x + 3|) - 5 meet 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) = -2e^(-2(2(2|((-3x - 3)/(-1x - 3)) - 1| - 2) - 3)) and g(x) = 1((-1(-2x^2 + 2) + 3)/(-1(-2x^2 + 2) + 2)) - 3 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) = 2|(-2(2e^(-1(5x + 4)) - 2)^2 - 5(2e^(-1(5x + 4)) - 2) + 1)| + 1 and g(x) = -3((1(-1|x + 1| + 3))/(1(-1|x + 1| + 3) - 2)) - 4 intersect in the range -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 0 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (-3(1(-1x + 3)^2 + 2(-1x + 3) - 1) + 3)/(2(1(-1x + 3)^2 + 2(-1x + 3) - 1) + 1) and g(x) = (1(-2cos(1πx - 1) - 1) + 2)/(-1(-2cos(1πx - 1) - 1) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format... | 2 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 5(2|((1(-3x) - 2)/(-1(-3x) + 3))| + 1)^2 - 4(2|((1(-3x) - 2)/(-1(-3x) + 3))| + 1) - 3 and g(x) = (2(-1(1sin(1πx + 2)) - 2) - 3)/(2(-1(1sin(1πx + 2)) - 2)) meet in the interval [-10, 10]?\n\nPres... | -1 | MATH |
[
{
"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (1(3(-2|x + 3| - 2)^2 - 4(-2|x + 3| - 2) + 2) + 1)/(3(3(-2|x + 3| - 2)^2 - 4(-2|x + 3| - 2) + 2) + 3) and g(x) = 2|(2x - 4) - 3| meet in the interval [-10, 10]?\n\nPresent the answer in LaTex fo... | 4 | MATH |
[
{
"content": "If you add up all the x-coordinates where the functions f(x) = 4(-4(1|((3x + 1)/(-1x)) - 3|)^2 + 2(1|((3x + 1)/(-1x)) - 3|) + 3) - 4 and g(x) = -1cos(2π(4((-2x + 1)/(2x))) - 1) - 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex form... | 0 | MATH |
[
{
"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -4(1|((1(-1x + 4) + 3)/(-2(-1x + 4))) - 1| - 2)^2 + 1(1|((1(-1x + 4) + 3)/(-2(-1x + 4))) - 1| - 2) + 2 and g(x) = -2(5(-1|x + 1| - 2)^2 - 4(-1|x + 1| - 2) + 4) + 4 in the interval [-10, 10], rounded to the... | 4 | MATH |
[
{
"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1sin(2π(-3|((-3(1x + 4) + 2)/(-2(1x + 4) + 1)) + 1| + 3) + 2) - 2 and g(x) = -1(1((-3x)/(1x + 2)) - 5)^2 + 4(1((-3x)/(1x + 2)) - 5) - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\... | -1 | MATH |
[
{
"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1|(-1(-5((-1x - 3)/(3x - 2))^2 - 5((-1x - 3)/(3x - 2)) - 5) + 2)| + 1 and g(x) = (-3(-2|(1x + 4) + 2| - 1))/(1(-2|(1x + 4) + 2| - 1) + 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\b... | -12 | MATH |
[
{
"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -3cos(2π((-1(-2x^2 - 3x + 2) + 1)/(-1(-2x^2 - 3x + 2) - 3)) - 3) + 2 and g(x) = -4(-1x^2 + 3x + 5) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 5 | MATH |
[
{
"content": "At what integer value (rounded) do the functions f(x) = -1(-1|(1e^(2(-4x^2 + 1x + 4)) - 1) - 3| - 3) and g(x) = (3(3(3e^(-1x) - 2)^2 + 5(3e^(-1x) - 2) - 1) + 3)/(-2(3(3e^(-1x) - 2)^2 + 5(3e^(-1x) - 2) - 1) - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{You... | 2 | MATH |
[
{
"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (-3(-5(1(-1|x + 3| - 2) - 5)^2 - 3(1(-1|x + 3| - 2) - 5)) - 3)/(1(-5(1(-1|x + 3| - 2) - 5)^2 - 3(1(-1|x + 3| - 2) - 5))) and g(x) = -1((1(4x^2 - 5x) + 3)/(-1(4x^2 - 5x) + 2)) + 1 intersect in the interval [-10, 10]?\n\nPr... | 0 | MATH |
[
{
"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3|(-1((3(-2x^2 + 4x - 4) + 3)/(-1(-2x^2 + 4x - 4) + 3)) + 3) + 3| and g(x) = -3(5(2e^(1x) - 3) + 2)^2 - 2(5(2e^(1x) - 3) + 2) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 0 | MATH |
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