messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "How many zeros does the function f(x) = 2(1(3|(-4((-2x - 3)/(-2x + 3))^2 - 4((-2x - 3)/(-2x + 3)) + 4) - 1|) - 4)^2 + 3(1(3|(-4((-2x - 3)/(-2x + 3))^2 - 4((-2x - 3)/(-2x + 3)) + 4) - 1|) - 4) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"rol... | 8 | MATH |
[
{
"content": "How many solutions does the equation 5(2sin(2π(1|(-2|((-1x + 3)/(-2x + 1)) - 3| + 1) + 3| - 2) - 1)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 82 | MATH |
[
{
"content": "How many solutions does the equation (-3((-3(4(-2(-3|x - 1| + 2)^2 + 1(-3|x - 1| + 2))^2 - 3) - 3)/(-1(4(-2(-3|x - 1| + 2)^2 + 1(-3|x - 1| + 2))^2 - 3) + 2)) + 3)/(-3((-3(4(-2(-3|x - 1| + 2)^2 + 1(-3|x - 1| + 2))^2 - 3) - 3)/(-1(4(-2(-3|x - 1| + 2)^2 + 1(-3|x - 1| + 2))^2 - 3) + 2)) + 4) = 0 have ... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(1sin(3π((1(3|(-1x - 3)|) + 1)/(-3(3|(-1x - 3)|))) - 3) + 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19 | MATH |
[
{
"content": "How many solutions does the equation (3(-3e^(2(1|(-4(-1|x| + 2)^2 - 3(-1|x| + 2) + 4)| - 1)) + 3) + 3)/(-2(-3e^(2(1|(-4(-1|x| + 2)^2 - 3(-1|x| + 2) + 4)| - 1)) + 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1π(-2(-3|(1((-2x - 3)/(-3x + 4))^2 + 3((-2x - 3)/(-3x + 4)) - 2) + 3| + 2)^2 + 4(-3|(1((-2x - 3)/(-3x + 4))^2 + 3((-2x - 3)/(-3x + 4)) - 2) + 3| + 2)) - 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 419 | MATH |
[
{
"content": "How many solutions does the equation 2|(2e^(-1((1(-1|(-1x + 2) - 3| + 2) - 2)/(3(-1|(-1x + 2) - 3| + 2) + 1))) - 3) + 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3((1(-1sin(2π(-1(-3x) - 2) - 3)) - 3)/(-2(-1sin(2π(-1(-3x) - 2) - 3)) - 2)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation 3cos(1π(-1|((-3(4((1x - 3)/(2x - 1))) - 2)/(3(4((1x - 3)/(2x - 1))))) - 1| - 3)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(2((2(2(-2sin(2πx - 2) + 1) - 5))/(2(2(-2sin(2πx - 2) + 1) - 5) - 3)) + 2)^2 + 1(2((2(2(-2sin(2πx - 2) + 1) - 5))/(2(2(-2sin(2πx - 2) + 1) - 5) - 3)) + 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 80 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(-2(-1(-2|(3x^2 - 5x - 3) + 3| + 3) + 4)^2 + 5(-1(-2|(3x^2 - 5x - 3) + 3| + 3) + 4) + 3) + 1)/(-1(-2(-1(-2|(3x^2 - 5x - 3) + 3| + 3) + 4)^2 + 5(-1(-2|(3x^2 - 5x - 3) + 3| + 3) + 4) + 3) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1((-2(-1(-3(-2|x + 1| + 1)^2) - 1) + 1)/(2(-1(-3(-2|x + 1| + 1)^2) - 1) + 1)) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation (-1(1|(2(1(1|x - 2|)^2 - 5(1|x - 2|) + 5)^2 + 3(1(1|x - 2|)^2 - 5(1|x - 2|) + 5) - 1) + 3| + 1) + 3)/(1(1|(2(1(1|x - 2|)^2 - 5(1|x - 2|) + 5)^2 + 3(1(1|x - 2|)^2 - 5(1|x - 2|) + 5) - 1) + 3| + 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in La... | 4 | MATH |
[
{
"content": "How many solutions does the equation -5(4(-4(3sin(3π(5x + 3) - 3) + 3) + 2)^2 + 2(-4(3sin(3π(5x + 3) - 3) + 3) + 2) - 3)^2 - 2(4(-4(3sin(3π(5x + 3) - 3) + 3) + 2)^2 + 2(-4(3sin(3π(5x + 3) - 3) + 3) + 2) - 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your a... | 120 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(1π(-4(-1(-4(1x - 1)) + 2)^2) - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1152 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(1π(-3|(2(2|((2x + 1)/(1x - 3)) - 1| + 1) + 3) - 1| + 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 325 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2(-2|((3(-5(2cos(2πx - 2) + 2)^2 - 3(2cos(2πx - 2) + 2)) + 1)/(2(-5(2cos(2πx - 2) + 2)^2 - 3(2cos(2πx - 2) + 2)) + 2)) + 1| - 1)^2 - 4(-2|((3(-5(2cos(2πx - 2) + 2)^2 - 3(2cos(2πx - 2) + 2)) + 1)/(2(-5(2cos(2πx - 2) + 2)^2 - 3(2cos(2πx - 2) + ... | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-4(-2cos(2π(-5(3x^2 + 2x) + 3)) + 1) + 5) + 3)/(-2(-4(-2cos(2π(-5(3x^2 + 2x) + 3)) + 1) + 5) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 734 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|((2(2sin(2π(1((1x + 1)/(1x - 2))^2 - 3((1x + 1)/(1x - 2)) - 4) + 3) - 1) + 3)/(1(2sin(2π(1((1x + 1)/(1x - 2))^2 - 3((1x + 1)/(1x - 2)) - 4) + 3) - 1) - 3)) + 1| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 225 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(1π(-1(-4(3|((-2x + 3)/(1x + 3)) - 1| - 1)^2 + 2(3|((-2x + 3)/(1x + 3)) - 1| - 1) - 4)^2 - 2(-4(3|((-2x + 3)/(1x + 3)) - 1| - 1)^2 + 2(3|((-2x + 3)/(1x + 3)) - 1| - 1) - 4) + 4) - 3) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex f... | 869 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (2((-1(4(-3|(1x - 3) - 3| + 3)^2 - 2(-3|(1x - 3) - 3| + 3)) + 2)/(-2(4(-3|(1x - 3) - 3| + 3)^2 - 2(-3|(1x - 3) - 3| + 3)) + 3)) + 2)/(2((-1(4(-3|(1x - 3) - 3| + 3)^2 - 2(-3|(1x - 3) - 3| + 3)) + 2)/(-2(4(-3|(1x - 3) - 3| + 3)^2 - 2(-3|(1x - 3)... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = (1(-4(2(-4(-1cos(1πx - 1))^2 - 3(-1cos(1πx - 1)) - 1)^2 + 1(-4(-1cos(1πx - 1))^2 - 3(-1cos(1πx - 1)) - 1) - 5) - 5) - 3)/(3(-4(2(-4(-1cos(1πx - 1))^2 - 3(-1cos(1πx - 1)) - 1)^2 + 1(-4(-1cos(1πx - 1))^2 - 3(-1cos(1πx - 1)) - 1) - 5) - 5) - 2) have in the inte... | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1π(-4(5(-5(5x^2 + 5x + 5)^2 + 5(5x^2 + 5x + 5) + 5) - 1) + 3) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 368 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2sin(1π(-1(1(-4((2x + 1)/(-3x + 4)) + 3) - 1)^2 + 3(1(-4((2x + 1)/(-3x + 4)) + 3) - 1) - 3)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(3sin(3π(2(-4(-4x^2 + 5x + 5)^2 - 3(-4x^2 + 5x + 5) + 3) + 5) - 1) + 3)^2 + 4(3sin(3π(2(-4(-4x^2 + 5x + 5)^2 - 3(-4x^2 + 5x + 5) + 3) + 5) - 1) + 3) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 382 | MATH |
[
{
"content": "How many zeros does the function f(x) = (1(-1(1(1|(2x^2 - 5x - 3) + 1| - 3)^2 - 3(1|(2x^2 - 5x - 3) + 1| - 3) - 3) + 5) + 1)/(1(-1(1(1|(2x^2 - 5x - 3) + 1| - 3)^2 - 3(1|(2x^2 - 5x - 3) + 1| - 3) - 3) + 5) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 6 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5((-2(-2|(-4(-1x^2 - 2x + 1) - 2)| + 2) - 1)/(-2(-2|(-4(-1x^2 - 2x + 1) - 2)| + 2) - 2))^2 - 1((-2(-2|(-4(-1x^2 - 2x + 1) - 2)| + 2) - 1)/(-2(-2|(-4(-1x^2 - 2x + 1) - 2)| + 2) - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\bo... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2((-3(2sin(3π(4(-1|x - 3| + 1) + 2) + 2) + 3))/(2(2sin(3π(4(-1|x - 3| + 1) + 2) + 2) + 3) + 3)) - 2)/(2((-3(2sin(3π(4(-1|x - 3| + 1) + 2) + 2) + 3))/(2(2sin(3π(4(-1|x - 3| + 1) + 2) + 2) + 3) + 3)) - 1) where -10 ≤ x ≤ 10.\n\nPresent the ans... | 240 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-4(2|(1|(5x^2 - 3x - 4) - 2| - 3) - 1| - 3) + 4) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1((-1(-1(1(1e^(-2x) + 3)^2 - 3) - 1) + 2)/(-1(-1(1(1e^(-2x) + 3)^2 - 3) - 1) - 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 61 | MATH |
[
{
"content": "How many solutions does the equation 2sin(1π(-3|(-1|(-4(-3|x + 3| + 1)^2 - 1(-3|x + 3| + 1) - 2)| + 3) + 1| - 3) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1425 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (2(1((2(-2|(1cos(1πx - 1) + 1)| + 1) + 1)/(1(-2|(1cos(1πx - 1) + 1)| + 1) + 1)) - 3) + 3)/(-3(1((2(-2|(1cos(1πx - 1) + 1)| + 1) + 1)/(1(-2|(1cos(1πx - 1) + 1)| + 1) + 1)) - 3) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\b... | 10 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(3π(3|(-1(-3(-1|x + 2| - 2)^2 + 4(-1|x + 2| - 2) + 2)^2 + 2(-3(-1|x + 2| - 2)^2 + 4(-1|x + 2| - 2) + 2) - 5) - 2| - 1) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 564 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(1sin(2π(5(-3|(5x - 5)| - 1)^2 - 4(-3|(5x - 5)| - 1) + 3) + 1) + 2) + 2)/(-1(1sin(2π(5(-3|(5x - 5)| - 1)^2 - 4(-3|(5x - 5)| - 1) + 3) + 1) + 2) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role... | 1453 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1cos(1π(1|(-1(2|(-1|x - 3| + 2) - 2| + 1)^2 + 2(2|(-1|x - 3| + 2) - 2| + 1) + 5) + 1| - 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 871 | MATH |
[
{
"content": "How many solutions does the equation -2e^(1(-3|(2(3(3x^2 - 5x - 4)^2 + 1(3x^2 - 5x - 4) + 2) - 1) - 3| + 2)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-4(-2sin(3π((3(-4x^2 + 3) - 3)/(1(-4x^2 + 3) + 1)) - 1) + 1) + 1) + 3)/(-3(-4(-2sin(3π((3(-4x^2 + 3) - 3)/(1(-4x^2 + 3) + 1)) - 1) + 1) + 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 30 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5(-1|((-2(-1cos(3π(-4x + 3) + 1)) + 3)/(1(-1cos(3π(-4x + 3) + 1)))) + 1| + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(3π((1(2|((-2((-1x + 2)/(-2x + 3)) + 2)/(3((-1x + 2)/(-2x + 3)) + 1)) + 3| - 3) + 1)/(1(2|((-2((-1x + 2)/(-2x + 3)) + 2)/(3((-1x + 2)/(-2x + 3)) + 1)) + 3| - 3) + 2)) - 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\b... | 7 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3π(-4((-3(-1|(-3|x - 1|) + 2| + 1) + 3)/(3(-1|(-3|x - 1|) + 2| + 1) - 2)) + 1) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 115 | MATH |
[
{
"content": "How many solutions does the equation 2e^(-2(1|(5((3(-2x + 5))/(-2(-2x + 5) - 3))^2 - 5((3(-2x + 5))/(-2(-2x + 5) - 3)) - 5) - 2| + 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5((-2(-5(2sin(1π(-1x^2 - 3x - 2) + 1) - 1) + 2) - 3)/(1(-5(2sin(1π(-1x^2 - 3x - 2) + 1) - 1) + 2))) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 186 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(2cos(2π((-3(-1|(-1x + 4)|) - 3)/(2(-1|(-1x + 4)|) + 1)) - 2) + 1)^2 - 2(2cos(2π((-3(-1|(-1x + 4)|) - 3)/(2(-1|(-1x + 4)|) + 1)) - 2) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 106 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(2π(5(2|(2(-2|x - 1| + 2)^2 - 2(-2|x - 1| + 2) + 4) - 3| + 1)^2 + 3(2|(2(-2|x - 1| + 2)^2 - 2(-2|x - 1| + 2) + 4) - 3| + 1) + 4) - 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
... | 370 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1((-1(1(-4(2sin(1πx + 2) + 2) + 5) + 2) + 3)/(-3(1(-4(2sin(1πx + 2) + 2) + 5) + 2))) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(-3(-2(-1|(-1x^2 - 5x + 1) - 2| + 1)^2 + 3(-1|(-1x^2 - 5x + 1) - 2| + 1) + 2) + 5) - 1)/(1(-3(-2(-1|(-1x^2 - 5x + 1) - 2| + 1)^2 + 3(-1|(-1x^2 - 5x + 1) - 2| + 1) + 2) + 5) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxe... | 4 | MATH |
[
{
"content": "How many solutions does the equation 1(-3(-2sin(2π(1(-3x^2 + 4x)^2 - 2(-3x^2 + 4x) + 1) + 2) + 2) + 5) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 847 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2(1|(-2|((2(4x^2 + 3x - 4) - 2)/(1(4x^2 + 3x - 4) + 2)) + 3| + 2) + 3| - 3))/(2(1|(-2|((2(4x^2 + 3x - 4) - 2)/(1(4x^2 + 3x - 4) + 2)) + 3| + 2) + 3| - 3) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(1π(-5(-5(-1|((1x - 1)/(-2x + 1)) - 3| - 3)^2 + 5)) - 1) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 277 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((2((1(-3cos(1π(5x^2 + 4x + 4))) + 2)/(-1(-3cos(1π(5x^2 + 4x + 4))) + 3)) - 2)/(3((1(-3cos(1π(5x^2 + 4x + 4))) + 2)/(-1(-3cos(1π(5x^2 + 4x + 4))) + 3)) - 2)) + 3)/(1((2((1(-3cos(1π(5x^2 + 4x + 4))) + 2)/(-1(-3cos(1π(5x^2 + 4x + 4))) + 3... | 155 | MATH |
[
{
"content": "How many solutions does the equation 1(2(1(-3sin(3π(3x^2 + 5) + 1) + 3)^2 - 3(-3sin(3π(3x^2 + 5) + 1) + 3) + 1)^2 - 4(1(-3sin(3π(3x^2 + 5) + 1) + 3)^2 - 3(-3sin(3π(3x^2 + 5) + 1) + 3) + 1) - 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 937 | MATH |
[
{
"content": "How many zeros does the function f(x) = (1(3((-1(-3(-2e^(-2x) + 2)^2 + 1(-2e^(-2x) + 2) + 1) + 2)/(3(-3(-2e^(-2x) + 2)^2 + 1(-2e^(-2x) + 2) + 1)))^2 + 1((-1(-3(-2e^(-2x) + 2)^2 + 1(-2e^(-2x) + 2) + 1) + 2)/(3(-3(-2e^(-2x) + 2)^2 + 1(-2e^(-2x) + 2) + 1))) - 3) + 3)/(-1(3((-1(-3(-2e^(-2x) + 2)^2 + 1... | 14 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(2(2|(1cos(2π(-1|x + 1| - 2) + 2)) - 2| - 3) - 1) - 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2(1(3(-2|(1|x + 3| + 1) - 3| + 1)^2 - 1(-2|(1|x + 3| + 1) - 3| + 1) - 4) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(1(1(-3(1x - 3)^2 - 4(1x - 3))^2 + 2(-3(1x - 3)^2 - 4(1x - 3)) - 3)^2 - 3(1(-3(1x - 3)^2 - 4(1x - 3))^2 + 2(-3(1x - 3)^2 - 4(1x - 3)) - 3) - 3)^2 - 4(1(1(-3(1x - 3)^2 - 4(1x - 3))^2 + 2(-3(1x - 3)^2 - 4(1x - 3)) - 3)^2 - 3(1(-3(1x - 3)^2 - 4(1x - 3))^2 + 2... | 12 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(-2sin(3π((2((2((-2x + 3)/(3x - 2)) - 2)/(-2((-2x + 3)/(3x - 2)) + 3)) + 1)/(1((2((-2x + 3)/(3x - 2)) - 2)/(-2((-2x + 3)/(3x - 2)) + 3)) - 2))) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role"... | 11 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(3e^(2(-4(1(-2x^2 - 3x + 5)^2 - 5(-2x^2 - 3x + 5) - 4)^2 + 4(1(-2x^2 - 3x + 5)^2 - 5(-2x^2 - 3x + 5) - 4) - 2)) - 3) + 2| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3((3(-5(-5(-1x^2 - 2x + 1) + 4)^2 + 3(-5(-1x^2 - 2x + 1) + 4)) + 1)/(3(-5(-5(-1x^2 - 2x + 1) + 4)^2 + 3(-5(-1x^2 - 2x + 1) + 4)) - 2)) + 1)/(2((3(-5(-5(-1x^2 - 2x + 1) + 4)^2 + 3(-5(-1x^2 - 2x + 1) + 4)) + 1)/(3(-5(-5(-1x^2 - 2x + 1) + 4)^2 + 3(-5(-1x^2 - 2... | 4 | MATH |
[
{
"content": "How many solutions does the equation (-2(-2((3(-2|(-2x^2 + 2x - 2) + 1| + 2) + 3)/(1(-2|(-2x^2 + 2x - 2) + 1| + 2)))^2 + 1((3(-2|(-2x^2 + 2x - 2) + 1| + 2) + 3)/(1(-2|(-2x^2 + 2x - 2) + 1| + 2))) + 1))/(-3(-2((3(-2|(-2x^2 + 2x - 2) + 1| + 2) + 3)/(1(-2|(-2x^2 + 2x - 2) + 1| + 2)))^2 + 1((3(-2|(-2x... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(5(2cos(1π(4(-3|x + 3| - 3)^2 + 2(-3|x + 3| - 3)) - 1) + 1) - 1) + 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 540 | MATH |
[
{
"content": "How many solutions does the equation (-1(3sin(3π(-2(-2(-1x - 5) - 1)^2 + 4(-2(-1x - 5) - 1) + 3) - 3) + 1) + 1)/(2(3sin(3π(-2(-2(-1x - 5) - 1)^2 + 4(-2(-1x - 5) - 1) + 3) - 3) + 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user... | 1054 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1π(-2(-4(2|(3|x - 3| - 2) - 2| - 2)^2 + 4(2|(3|x - 3| - 2) - 2| - 2))^2 + 1(-4(2|(3|x - 3| - 2) - 2| - 2)^2 + 4(2|(3|x - 3| - 2) - 2| - 2)) + 3) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"... | 355 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(1|(-3|(3|(3x^2 - 2x + 2) - 2| + 1) - 1| - 3) + 3|) + 1)/(3(1|(-3|(3|(3x^2 - 2x + 2) - 2| + 1) - 1| - 3) + 3|) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -2|(-2cos(1π(1(3|(4x + 3) - 3| - 2)^2 + 4(3|(4x + 3) - 3| - 2) + 5) + 3) - 1) + 1| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 921 | MATH |
[
{
"content": "How many solutions does the equation (-1(2sin(2π(2|((1(2x^2 - 4x - 4) - 3)/(-1(2x^2 - 4x - 4) - 3)) - 1| + 1) + 2) - 1) + 1)/(-2(2sin(2π(2|((1(2x^2 - 4x - 4) - 3)/(-1(2x^2 - 4x - 4) - 3)) - 1| + 1) + 2) - 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your ... | 86 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(-1(3sin(3π(2(3x - 3)^2 - 2(3x - 3) - 5)) - 2) - 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1142 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3(-3cos(3π(-5(-2(-5x - 5) - 3) - 2)) + 1) + 1)/(1(-3cos(3π(-5(-2(-5x - 5) - 3) - 2)) + 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 426 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(1sin(2π(-4(3|(-1x + 2) + 3| - 2)^2 + 2(3|(-1x + 2) + 3| - 2) - 4) + 3) + 2)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1088 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(3(3|(1|(3x^2 - 1x - 4) - 2| - 1) - 2|)^2) + 2)/(-3(3(3|(1|(3x^2 - 1x - 4) - 2| - 1) - 2|)^2) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(1(2(2|((-1x - 2)/(-2x + 3)) - 3| + 1)^2 - 3(2|((-1x - 2)/(-2x + 3)) - 3| + 1) - 2)^2 - 5(2(2|((-1x - 2)/(-2x + 3)) - 3| + 1)^2 - 3(2|((-1x - 2)/(-2x + 3)) - 3| + 1) - 2) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\box... | 4 | MATH |
[
{
"content": "How many solutions does the equation -3sin(2π(1|(2|(2((-2x - 3)/(3x - 2)))|) + 3|) - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 70 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2((1(-4(2sin(2π(-4x^2 - 1x - 3) - 1))^2 - 5(2sin(2π(-4x^2 - 1x - 3) - 1)) + 1) - 3)/(3(-4(2sin(2π(-4x^2 - 1x - 3) - 1))^2 - 5(2sin(2π(-4x^2 - 1x - 3) - 1)) + 1) - 2))^2 + 2((1(-4(2sin(2π(-4x^2 - 1x - 3) - 1))^2 - 5(2sin(2π(-4x^2 - 1x - 3) - 1)... | 548 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1((3(-2cos(1π(-1(2|x + 3| - 3) + 4) - 2)))/(-2(-2cos(1π(-1(2|x + 3| - 3) + 4) - 2)) - 1))^2 + 1((3(-2cos(1π(-1(2|x + 3| - 3) + 4) - 2)))/(-2(-2cos(1π(-1(2|x + 3| - 3) + 4) - 2)) - 1)) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex for... | 40 | MATH |
[
{
"content": "How many solutions does the equation -5(3|(-3|(-2(-2cos(3πx - 3) + 1) + 4) - 2|) + 1| - 1)^2 - 3(3|(-3|(-2(-2cos(3πx - 3) + 1) + 4) - 2|) + 1| - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 91 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(5(-3sin(1π((-2(-2x^2 - 3x - 5) - 2)/(-1(-2x^2 - 3x - 5) - 3)) + 3) - 1)) + 3)/(-3(5(-3sin(1π((-2(-2x^2 - 3x - 5) - 2)/(-1(-2x^2 - 3x - 5) - 3)) + 3) - 1)) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 10 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(-1e^(1((2(-5(-1|x + 2| + 2)^2 + 3(-1|x + 2| + 2) + 2) + 2)/(-2(-5(-1|x + 2| + 2)^2 + 3(-1|x + 2| + 2) + 2) - 1))) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(-2|(-3(3|(2|x + 1| - 3) - 1|) + 3) + 2| - 2)^2 - 4(-2|(-3(3|(2|x + 1| - 3) - 1|) + 3) + 2| - 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|(-3(1|(2(-3|x + 3| + 3) + 4) - 1| - 2) - 1) + 2| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1e^(2(-1(-3(1(-2x + 3)^2 + 2(-2x + 3) - 1)^2 - 4(1(-2x + 3)^2 + 2(-2x + 3) - 1) + 1) - 2)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(2π(1(-2(4(2x^2 - 1x + 1)^2 + 3(2x^2 - 1x + 1) - 2) - 5) + 2) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1173 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4(2|(4(-3|(4x^2 - 1x - 3) + 2| + 2) + 3) - 2| - 2) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many solutions does the equation -1(-1(1(3|((2x + 3)/(-2x - 2)) + 1| - 2)^2 - 3)^2 - 5(1(3|((2x + 3)/(-2x - 2)) + 1| - 2)^2 - 3)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(-2cos(3π(1|(-2|((-2x - 1)/(-3x - 3)) - 1| + 3)| - 1) + 3) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(4((3(-4(1|x - 2| - 3)))/(-1(-4(1|x - 2| - 3)) - 1))^2 + 1((3(-4(1|x - 2| - 3)))/(-1(-4(1|x - 2| - 3)) - 1)) + 5)^2 + 4(4((3(-4(1|x - 2| - 3)))/(-1(-4(1|x - 2| - 3)) - 1))^2 + 1((3(-4(1|x - 2| - 3)))/(-1(-4(1|x - 2| - 3)) - 1)) + 5) + 5 have in the interva... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(1((1(-1(-3sin(1πx - 1) + 1)^2 + 3(-3sin(1πx - 1) + 1)) - 3)/(-1(-1(-3sin(1πx - 1) + 1)^2 + 3(-3sin(1πx - 1) + 1)) - 2))^2 - 2((1(-1(-3sin(1πx - 1) + 1)^2 + 3(-3sin(1πx - 1) + 1)) - 3)/(-1(-1(-3sin(1πx - 1) + 1)^2 + 3(-3sin(1πx - 1) + 1)... | 40 | MATH |
[
{
"content": "How many solutions does the equation (3(2sin(2π(-2(1|((2x - 3)/(3x + 1)) + 1| + 2)^2 + 4(1|((2x - 3)/(3x + 1)) + 1| + 2) - 1)) - 2))/(-2(2sin(2π(-2(1|((2x - 3)/(3x + 1)) + 1| + 2)^2 + 4(1|((2x - 3)/(3x + 1)) + 1| + 2) - 1)) - 2) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex ... | 123 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-1(-1sin(2π(-2|(-5x + 1) + 3|) + 3) - 3)^2 - 3(-1sin(2π(-2|(-5x + 1) + 3|) + 3) - 3) + 3) - 3)/(2(-1(-1sin(2π(-2|(-5x + 1) + 3|) + 3) - 3)^2 - 3(-1sin(2π(-2|(-5x + 1) + 3|) + 3) - 3) + 3) + 2) equals zero.\n\nPresent the answer in LaTex... | 399 | MATH |
[
{
"content": "How many solutions does the equation (-2(-1|(2sin(2π(3|(2x)| - 1) - 1) + 3) - 2| + 1) - 3)/(-1(-1|(2sin(2π(3|(2x)| - 1) - 1) + 3) - 2| + 1) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "How many solutions does the equation -3|(-2|(2|((-3(-5x + 2) - 1)/(-1(-5x + 2) + 3)) + 3| - 2) + 1| + 3) + 1| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(2|((2((1(-2x^2 + 4) + 2)/(2(-2x^2 + 4) + 1)) + 1)/(-3((1(-2x^2 + 4) + 2)/(2(-2x^2 + 4) + 1)) - 1))| - 3)^2 - 2(2|((2((1(-2x^2 + 4) + 2)/(2(-2x^2 + 4) + 1)) + 1)/(-3((1(-2x^2 + 4) + 2)/(2(-2x^2 + 4) + 1)) - 1))| - 3) + 2 equals zero.\n\n... | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(3π(2(-3((-2(-2|x - 3| + 3) + 1)/(-1(-2|x - 3| + 3) - 1))^2 - 2((-2(-2|x - 3| + 3) + 1)/(-1(-2|x - 3| + 3) - 1)) - 1) + 5) + 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 569 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3((2(-5(1x^2 - 3x - 5) - 2))/(-2(-5(1x^2 - 3x - 5) - 2) + 3))^2 + 5((2(-5(1x^2 - 3x - 5) - 2))/(-2(-5(1x^2 - 3x - 5) - 2) + 3))) + 3)/(3(3((2(-5(1x^2 - 3x - 5) - 2))/(-2(-5(1x^2 - 3x - 5) - 2) + 3))^2 + 5((2(-5(1x^2 - 3x - 5) - 2))/(-2(... | 4 | MATH |
[
{
"content": "How many solutions does the equation 4(5(-2(-1|(-1|x + 1| + 1) + 3| + 1)^2 + 4(-1|(-1|x + 1| + 1) + 3| + 1) + 4) + 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(3cos(3π(-3|((-2(-1x - 3) + 1)/(2(-1x - 3))) + 2| - 3) - 1) + 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5(-2|(4(-5(-2|x - 2|) - 3)^2 - 1(-5(-2|x - 2|) - 3) - 1) - 2| + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(-1(3(5((1x + 1)/(-1x - 3))^2 - 1((1x + 1)/(-1x - 3)) - 4) + 1)^2 + 5(3(5((1x + 1)/(-1x - 3))^2 - 1((1x + 1)/(-1x - 3)) - 4) + 1) + 3) + 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"... | 6 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(1(3|(-3(-3e^(2x))^2 - 2(-3e^(2x)) + 5) + 2| - 2)^2 - 5(3|(-3(-3e^(2x))^2 - 2(-3e^(2x)) + 5) + 2| - 2) + 5) - 2| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(1(-2(-2(-1x + 3)^2 - 4(-1x + 3) + 2)^2 - 5(-2(-1x + 3)^2 - 4(-1x + 3) + 2) + 1)^2 - 3(-2(-2(-1x + 3)^2 - 4(-1x + 3) + 2)^2 - 5(-2(-1x + 3)^2 - 4(-1x + 3) + 2) + 1) + 4) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{You... | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|(5(-1|(-2cos(3π((-1x + 1)/(-3x - 1)) + 1) - 1) - 1| + 1) + 1)| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3sin(1π((1((1(3(2|x + 3| + 1)^2 - 4(2|x + 3| + 1) - 3) + 2)/(3(3(2|x + 3| + 1)^2 - 4(2|x + 3| + 1) - 3) + 1)) + 2)/(-2((1(3(2|x + 3| + 1)^2 - 4(2|x + 3| + 1) - 3) + 2)/(3(3(2|x + 3| + 1)^2 - 4(2|x + 3| + 1) - 3) + 1)) + 1)) + 3) + 3 have in the interval [-10... | 40 | MATH |
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