messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "How many zeros does the function f(x) = (-3(-2(-1(3sin(2π((-2(-1x^2 + 1x + 4) + 3)/(-3(-1x^2 + 1x + 4) + 4)) - 2) + 1)^2 + 2(3sin(2π((-2(-1x^2 + 1x + 4) + 3)/(-3(-1x^2 + 1x + 4) + 4)) - 2) + 1) + 1) + 3) + 1)/(-2(-2(-1(3sin(2π((-2(-1x^2 + 1x + 4) + 3)/(-3(-1x^2 + 1x + 4) + 4)) - 2) + 1)^2 + 2(3sin... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(1sin(1π(-1|(-1|(-3(4x^2 - 5x - 3) - 4) - 3| + 3) - 3| - 2) - 1) - 1) - 1| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 952 | MATH |
[
{
"content": "How many solutions does the equation (2(-4(1(3sin(2π((-1(-5x^2 - 3x - 2) - 3)/(-3(-5x^2 - 3x - 2) - 2)) + 2) + 3) - 5) + 4) - 2)/(-1(-4(1(3sin(2π((-1(-5x^2 - 3x - 2) - 3)/(-3(-5x^2 - 3x - 2) - 2)) + 2) + 3) - 5) + 4) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\bo... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-2((-2(3sin(3π(1|((1x - 3)/(1x + 3))| - 1) + 1) + 1) - 3)/(-3(3sin(3π(1|((1x - 3)/(1x + 3))| - 1) + 1) + 1) - 2)) + 2) - 2 have in the interval [-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) = -3sin(2π(3|(-1|(-3(-1(-1|x - 3| - 2)^2 - 5(-1|x - 3| - 2) - 2)^2 - 4(-1(-1|x - 3| - 2)^2 - 5(-1|x - 3| - 2) - 2) - 4) - 2| - 2) + 1| - 1) - 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "u... | 1264 | MATH |
[
{
"content": "How many solutions does the equation (3(2cos(3π((1(3(1(3x^2 + 5x - 1)^2 - 1(3x^2 + 5x - 1) - 5)^2 + 5) + 3)/(3(3(1(3x^2 + 5x - 1)^2 - 1(3x^2 + 5x - 1) - 5)^2 + 5) - 1)) + 1) - 2) + 2)/(1(2cos(3π((1(3(1(3x^2 + 5x - 1)^2 - 1(3x^2 + 5x - 1) - 5)^2 + 5) + 3)/(3(3(1(3x^2 + 5x - 1)^2 - 1(3x^2 + 5x - 1) ... | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-2((3(-3(-1|(-3|x - 2| + 1)|)^2 + 5(-1|(-3|x - 2| + 1)|) + 4) - 2)/(-1(-3(-1|(-3|x - 2| + 1)|)^2 + 5(-1|(-3|x - 2| + 1)|) + 4) - 1)) + 5)^2 - 4(-2((3(-3(-1|(-3|x - 2| + 1)|)^2 + 5(-1|(-3|x - 2| + 1)|) + 4) - 2)/(-1(-3(-1|(-3|x - 2| + 1)|... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(1π(3(-5(1|(-1|((3x + 3)/(-1x + 2)) + 2|) + 1| - 2)^2 - 2(1|(-1|((3x + 3)/(-1x + 2)) + 2|) + 1| - 2) + 4) + 5) - 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 334 | MATH |
[
{
"content": "How many solutions does the equation (-1(1|(-1|(3(5(-2|x + 3| + 1)^2 + 3(-2|x + 3| + 1) - 5)^2 + 5(5(-2|x + 3| + 1)^2 + 3(-2|x + 3| + 1) - 5) - 4)| - 2) + 2| + 1) + 2)/(3(1|(-1|(3(5(-2|x + 3| + 1)^2 + 3(-2|x + 3| + 1) - 5)^2 + 5(5(-2|x + 3| + 1)^2 + 3(-2|x + 3| + 1) - 5) - 4)| - 2) + 2| + 1) + 3) ... | 16 | MATH |
[
{
"content": "How many solutions does the equation -2cos(1π(-5(3((-1(-2(-1x - 1)^2 + 4) + 2)/(-1(-2(-1x - 1)^2 + 4) - 1))^2 + 5((-1(-2(-1x - 1)^2 + 4) + 2)/(-1(-2(-1x - 1)^2 + 4) - 1)) + 2) - 4) + 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "... | 157 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(-5((3(2|(-3cos(3π((2x - 2)/(-1x - 2)) - 2)) - 1| - 1))/(-3(2|(-3cos(3π((2x - 2)/(-1x - 2)) - 2)) - 1| - 1) - 3))^2 + 2((3(2|(-3cos(3π((2x - 2)/(-1x - 2)) - 2)) - 1| - 1))/(-3(2|(-3cos(3π((2x - 2)/(-1x - 2)) - 2)) - 1| - 1) - 3)) + 2) - 2 whe... | 151 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(2cos(1π(4(2|(-3((3x + 1)/(3x + 2))^2 - 5((3x + 1)/(3x + 2)) - 3) + 1| + 3)^2 + 4(2|(-3((3x + 1)/(3x + 2))^2 - 5((3x + 1)/(3x + 2)) - 3) + 1| + 3) + 4) + 1) - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 944 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2(3sin(2π(-3|(2(4(1x^2 - 4) - 4) + 5) - 2| + 1) - 3)) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1000 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(3π(4(2|(3|(3(3|x + 3| + 1) - 5) - 3| + 3) + 3| + 1)^2 + 3(2|(3|(3(3|x + 3| + 1) - 5) - 3| + 3) + 3| + 1) + 2) - 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 329 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3((-3(-2cos(1π(3(2(2|x - 2|) - 4) - 1) + 3) + 2) + 1)/(-2(-2cos(1π(3(2(2|x - 2|) - 4) - 1) + 3) + 2) - 2)) + 1)/(-1((-3(-2cos(1π(3(2(2|x - 2|) - 4) - 1) + 3) + 2) + 1)/(-2(-2cos(1π(3(2(2|x - 2|) - 4) - 1) + 3) + 2) - 2))) equals zero.\n\... | 240 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|((3(-2(3sin(3π((1(-2|x - 1| + 3) - 1)/(-3(-2|x - 1| + 3) - 2)) - 2) - 1)^2 - 3(3sin(3π((1(-2|x - 1| + 3) - 1)/(-3(-2|x - 1| + 3) - 2)) - 2) - 1) + 1))/(-1(-2(3sin(3π((1(-2|x - 1| + 3) - 1)/(-3(-2|x - 1| + 3) - 2)) - 2) - 1)^2 - 3(3sin(3π((1... | 15 | MATH |
[
{
"content": "How many solutions does the equation -1((3(-1(-3|(-2|((-2x)/(1x + 2)) - 3|) + 2| + 1)^2 - 2(-3|(-2|((-2x)/(1x + 2)) - 3|) + 2| + 1) + 1) - 3)/(-1(-1(-3|(-2|((-2x)/(1x + 2)) - 3|) + 2| + 1)^2 - 2(-3|(-2|((-2x)/(1x + 2)) - 3|) + 2| + 1) + 1) + 2))^2 + 4((3(-1(-3|(-2|((-2x)/(1x + 2)) - 3|) + 2| + 1)^... | 16 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(1cos(2π(-2|(1(2|(-2|x - 3| + 1) + 1| + 2) - 1) + 1| + 1) + 1)) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(3(-2|((3(-2|(2e^(2x) + 2) - 3| + 1) + 1)/(1(-2|(2e^(2x) + 2) - 3| + 1) - 2)) + 2|) + 5) + 5 equals zero.\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(2(-2(-2|((1x + 3)/(3x)) - 2| + 1)^2 - 5(-2|((1x + 3)/(3x)) - 2| + 1) + 4)^2 - 3(-2(-2|((1x + 3)/(3x)) - 2| + 1)^2 - 5(-2|((1x + 3)/(3x)) - 2| + 1) + 4) - 2) - 4) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Yo... | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(2(2(4(2sin(3π(5x)) + 2)^2 - 1(2sin(3π(5x)) + 2) - 3) + 1) - 1) + 2| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 321 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4(1|(2(-1(4(3|x|))^2 - 4(4(3|x|)) + 5) + 1) + 1| - 2) + 3 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) = 1|(-1|(-1|(2|(-3(-3|x + 1| + 3)^2 - 5(-3|x + 1| + 3) + 1) + 3| - 3) + 3| - 1) - 2| + 1) + 2| - 3 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) = -3((-2(1|(-1(-2(-4x - 4)^2 - 1(-4x - 4) + 3)^2 - 2(-2(-4x - 4)^2 - 1(-4x - 4) + 3) - 2) + 3| - 2) + 2)/(-2(1|(-1(-2(-4x - 4)^2 - 1(-4x - 4) + 3)^2 - 2(-2(-4x - 4)^2 - 1(-4x - 4) + 3) - 2) + 3| - 2) - 1))^2 + 3((-2(1|(-1(-2(-4x - 4)^2 - 1(-4x - 4) + 3)^2 - 2(... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -5((-2(1|(-2|(-2(-2cos(1πx - 2) - 1) - 4) - 2|) - 2| - 3) - 2)/(1(1|(-2|(-2(-2cos(1πx - 2) - 1) - 4) - 2|) - 2| - 3)))^2 - 4((-2(1|(-2|(-2(-2cos(1πx - 2) - 1) - 4) - 2|) - 2| - 3) - 2)/(1(1|(-2|(-2(-2cos(1πx - 2) - 1) - 4) - 2|) - 2| - 3))... | 10 | MATH |
[
{
"content": "How many solutions does the equation -2(-1(-1(-2cos(2π(-2|(3x - 3) + 2| + 1) - 3) + 1) + 2) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 119 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3|(-3sin(2π(-2(-4(-2|(2x^2 + 4x - 4) + 1| + 3) - 4)^2 + 5) - 2) - 1)| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 282 | MATH |
[
{
"content": "How many solutions does the equation (-2(4(2((2((1(1x^2 - 2x - 2) + 2)/(1(1x^2 - 2x - 2) + 3)))/(-1((1(1x^2 - 2x - 2) + 2)/(1(1x^2 - 2x - 2) + 3)) + 2))^2 + 3((2((1(1x^2 - 2x - 2) + 2)/(1(1x^2 - 2x - 2) + 3)))/(-1((1(1x^2 - 2x - 2) + 2)/(1(1x^2 - 2x - 2) + 3)) + 2)) - 1)^2 + 1(2((2((1(1x^2 - 2x - ... | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4(-2cos(3π(5(1|(-1|(-1x^2 - 2x - 4)|) + 1| - 3)^2 - 2(1|(-1|(-1x^2 - 2x - 4)|) + 1| - 3)) + 2) + 2)^2 - 1(-2cos(3π(5(1|(-1|(-1x^2 - 2x - 4)|) + 1| - 3)^2 - 2(1|(-1|(-1x^2 - 2x - 4)|) + 1| - 3)) + 2) + 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the... | 604 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(3(2sin(2π(2|(-3|(-1x + 3) + 2| + 1) + 2| - 1) - 3) - 1)^2 + 4(2sin(2π(2|(-3|(-1x + 3) + 2| + 1) + 2| - 1) - 3) - 1) - 3) - 2| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 720 | MATH |
[
{
"content": "How many solutions does the equation 2|(-2(-5(2((-2((-1x + 1)/(2x)))/(-1((-1x + 1)/(2x)) + 2))^2 + 1((-2((-1x + 1)/(2x)))/(-1((-1x + 1)/(2x)) + 2)) - 1) + 3)^2 + 3(-5(2((-2((-1x + 1)/(2x)))/(-1((-1x + 1)/(2x)) + 2))^2 + 1((-2((-1x + 1)/(2x)))/(-1((-1x + 1)/(2x)) + 2)) - 1) + 3)) - 1| - 3 = 0 have ... | 4 | MATH |
[
{
"content": "How many solutions does the equation 2sin(1π(4(-5(2|(-2|(3|x + 1|) - 2|) + 3| + 3)^2 - 3)^2 + 3(-5(2|(-2|(3|x + 1|) - 2|) + 3| + 3)^2 - 3) + 5)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(3((-2(-2|(-3(1x^2 - 4x + 4)^2 + 2(1x^2 - 4x + 4) + 1) + 2|) + 2)/(3(-2|(-3(1x^2 - 4x + 4)^2 + 2(1x^2 - 4x + 4) + 1) + 2|) + 2)) + 3)^2 - 3(3((-2(-2|(-3(1x^2 - 4x + 4)^2 + 2(1x^2 - 4x + 4) + 1) + 2|) + 2)/(3(-2|(-3(1x^2 - 4x + 4)^2 + 2(1x^2 -... | 6 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1sin(3π(-3(5((3(-1((-1x + 2)/(3x - 2)) - 3) + 2)/(1(-1((-1x + 2)/(3x - 2)) - 3) - 3)) + 5)^2 + 2(5((3(-1((-1x + 2)/(3x - 2)) - 3) + 2)/(1(-1((-1x + 2)/(3x - 2)) - 3) - 3)) + 5) - 5) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex form... | 232 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(-1(-1(-1(1sin(1π((1x - 1)/(-3x - 3)) + 2) + 3) - 1) - 3)^2 + 3(-1(-1(1sin(1π((1x - 1)/(-3x - 3)) + 2) + 3) - 1) - 3) - 1)^2 + 5(-1(-1(-1(1sin(1π((1x - 1)/(-3x - 3)) + 2) + 3) - 1) - 3)^2 + 3(-1(-1(1sin(1π((1x - 1)/(-3x - 3)) + 2) + 3) - 1) - 3) - 1) + 5 h... | 18 | MATH |
[
{
"content": "How many solutions does the equation 4((-1(-1|(-2(-2|(1x + 5) - 1| + 2) - 1) + 2| + 3) + 2)/(1(-1|(-2(-2|(1x + 5) - 1| + 2) - 1) + 2| + 3) + 1))^2 - 2((-1(-1|(-2(-2|(1x + 5) - 1| + 2) - 1) + 2| + 3) + 2)/(1(-1|(-2(-2|(1x + 5) - 1| + 2) - 1) + 2| + 3) + 1)) - 2 = 0 have in the range [-10, 10]?\n\nP... | 4 | MATH |
[
{
"content": "How many solutions does the equation -5(4((1(-4(3|(-2e^(-2x) + 2) + 3| - 3)^2 - 3(3|(-2e^(-2x) + 2) + 3| - 3) + 2) + 1)/(1(-4(3|(-2e^(-2x) + 2) + 3| - 3)^2 - 3(3|(-2e^(-2x) + 2) + 3| - 3) + 2) - 3))^2 + 5((1(-4(3|(-2e^(-2x) + 2) + 3| - 3)^2 - 3(3|(-2e^(-2x) + 2) + 3| - 3) + 2) + 1)/(1(-4(3|(-2e^(-... | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(-2|(2(-2|((1(-2x - 4) - 3)/(2(-2x - 4) - 1)) + 2| - 1) + 5)| + 2) + 2 where -10 ≤ x ≤ 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(3(-3(-3cos(3π(-1|(-2x^2 + 4) + 1| - 3) + 3) + 2) - 2) + 2) - 2)/(3(3(-3(-3cos(3π(-1|(-2x^2 + 4) + 1| - 3) + 3) + 2) - 2) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 82 | MATH |
[
{
"content": "How many zeros does the function f(x) = (2(1(-4(-2|(-2sin(2π(1x + 3) + 3) + 1) + 2| + 2)^2 + 5(-2|(-2sin(2π(1x + 3) + 3) + 1) + 2| + 2) + 2) - 3) + 3)/(2(1(-4(-2|(-2sin(2π(1x + 3) + 3) + 1) + 2| + 2)^2 + 5(-2|(-2sin(2π(1x + 3) + 3) + 1) + 2| + 2) + 2) - 3) - 1) have in the interval [-10, 10]?\n\nP... | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(1sin(2π((1((-2(1|((3x - 1)/(1x))| + 2) - 1)/(3(1|((3x - 1)/(1x))| + 2) - 2)))/(-3((-2(1|((3x - 1)/(1x))| + 2) - 1)/(3(1|((3x - 1)/(1x))| + 2) - 2)) - 2)) - 3) - 1) - 2)/(2(1sin(2π((1((-2(1|((3x - 1)/(1x))| + 2) - 1)/(3(1|((3x - 1)/(1x))| + 2) - 2)))/(-3(... | 19 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1e^(2(-2|(-3(1(-2(-5x^2 - 4x + 1)^2 - 5(-5x^2 - 4x + 1) - 4)^2 + 5(-2(-5x^2 - 4x + 1)^2 - 5(-5x^2 - 4x + 1) - 4) + 5)^2 - 3(1(-2(-5x^2 - 4x + 1)^2 - 5(-5x^2 - 4x + 1) - 4)^2 + 5(-2(-5x^2 - 4x + 1)^2 - 5(-5x^2 - 4x + 1) - 4) + 5) - 1) + 2| + 1... | 10 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(5(2|(-1((1(1x^2 + 3x - 5) + 2)/(1(1x^2 + 3x - 5) + 3))^2 + 1((1(1x^2 + 3x - 5) + 2)/(1(1x^2 + 3x - 5) + 3)) + 5) + 3| - 3)^2 + 3(2|(-1((1(1x^2 + 3x - 5) + 2)/(1(1x^2 + 3x - 5) + 3))^2 + 1((1(1x^2 + 3x - 5) + 2)/(1(1x^2 + 3x - 5) + 3)) + 5)... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3((-3(-1|((2(3|(2x^2 - 2x) - 1|) - 3)/(-1(3|(2x^2 - 2x) - 1|) - 1)) + 1|) - 1)/(-2(-1|((2(3|(2x^2 - 2x) - 1|) - 3)/(-1(3|(2x^2 - 2x) - 1|) - 1)) + 1|) + 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 6 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2(3|(-2(-3cos(2π(3|(3|x - 1| - 1) - 1| + 3)) + 2) - 1) + 3| - 1)^2 + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 512 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-3(-3sin(2π(-1|(-3(3(4x^2 - 5x + 2)^2 + 1(4x^2 - 5x + 2) + 4) + 3) + 1| + 2) + 2) - 2) + 2)/(3(-3sin(2π(-1|(-3(3(4x^2 - 5x + 2)^2 + 1(4x^2 - 5x + 2) + 4) + 3) + 1| + 2) + 2) - 2) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format:... | 71 | MATH |
[
{
"content": "How many solutions does the equation (-1(2((3(1((2(-2sin(3πx + 3) + 1) - 3)/(-3(-2sin(3πx + 3) + 1))) - 2) - 1)/(3(1((2(-2sin(3πx + 3) + 1) - 3)/(-3(-2sin(3πx + 3) + 1))) - 2) - 2)) - 1) - 1)/(-1(2((3(1((2(-2sin(3πx + 3) + 1) - 3)/(-3(-2sin(3πx + 3) + 1))) - 2) - 1)/(3(1((2(-2sin(3πx + 3) + 1) - 3... | 53 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(3sin(3π(-3|(1((-2(-3x^2 + 3x - 2) - 3)/(1(-3x^2 + 3x - 2)))^2 + 4((-2(-3x^2 + 3x - 2) - 3)/(1(-3x^2 + 3x - 2))) + 4) + 2| - 1)) - 3)^2 + 2(3sin(3π(-3|(1((-2(-3x^2 + 3x - 2) - 3)/(1(-3x^2 + 3x - 2)))^2 + 4((-2(-3x^2 + 3x - 2) - 3)/(1(-3x^... | 104 | MATH |
[
{
"content": "How many solutions does the equation 2sin(3π((1(1(-3|(-3((-3x + 1)/(-1x - 3))^2 - 1((-3x + 1)/(-1x - 3)) + 1) + 1| - 3) - 1) + 3)/(-2(1(-3|(-3((-3x + 1)/(-1x - 3))^2 - 1((-3x + 1)/(-1x - 3)) + 1) + 1| - 3) - 1) + 3)) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: ... | 6 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1((-1(-1|(3sin(1π(5(1x^2 + 2x + 2) + 1) - 3)) + 2| - 1) + 2)/(3(-1|(3sin(1π(5(1x^2 + 2x + 2) + 1) - 3)) + 2| - 1) + 2)) + 3)/(2((-1(-1|(3sin(1π(5(1x^2 + 2x + 2) + 1) - 3)) + 2| - 1) + 2)/(3(-1|(3sin(1π(5(1x^2 + 2x + 2) + 1) - 3)) + 2| - 1) + ... | 375 | MATH |
[
{
"content": "How many zeros does the function f(x) = (2(-2|(-2sin(1π(-1|(-2(-1x^2 + 3x - 2)^2 - 5(-1x^2 + 3x - 2) + 4) - 1|) + 2) + 1)| + 1) + 2)/(-3(-2|(-2sin(1π(-1|(-2(-1x^2 + 3x - 2)^2 - 5(-1x^2 + 3x - 2) + 4) - 1|) + 2) + 1)| + 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\bo... | 1253 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1cos(1π(-1((-3((3(2x + 4))/(-3(2x + 4) + 2)) + 2)/(-3((3(2x + 4))/(-3(2x + 4) + 2)) + 1)) - 5)) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "How many solutions does the equation -5(-4(-1|(-2|(1(-3x - 3) + 4) + 3| - 2) + 3| + 1)^2 - 1(-1|(-2|(1(-3x - 3) + 4) + 3| - 2) + 3| + 1) + 5)^2 - 4(-4(-1|(-2|(1(-3x - 3) + 4) + 3| - 2) + 3| + 1)^2 - 1(-1|(-2|(1(-3x - 3) + 4) + 3| - 2) + 3| + 1) + 5) + 5 = 0 have in the range [-10, 10]?\n\nPresent ... | 8 | MATH |
[
{
"content": "How many solutions does the equation 2cos(2π(-3((2((3(3|(1x^2 + 3)| - 3) + 1)/(-1(3|(1x^2 + 3)| - 3) + 2)) - 3)/(-1((3(3|(1x^2 + 3)| - 3) + 1)/(-1(3|(1x^2 + 3)| - 3) + 2)) - 2))^2 + 5((2((3(3|(1x^2 + 3)| - 3) + 1)/(-1(3|(1x^2 + 3)| - 3) + 2)) - 3)/(-1((3(3|(1x^2 + 3)| - 3) + 1)/(-1(3|(1x^2 + 3)| -... | 742 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3|((-2(2cos(2π(3(5(1x^2 - 3x - 4) + 5)^2 + 5(5(1x^2 - 3x - 4) + 5)) - 2) - 1) - 3)/(3(2cos(2π(3(5(1x^2 - 3x - 4) + 5)^2 + 5(5(1x^2 - 3x - 4) + 5)) - 2) - 1) + 3))| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",... | 4 | MATH |
[
{
"content": "How many solutions does the equation 3(1(3(2|((1(-1e^(-2x)) - 2)/(2(-1e^(-2x)) + 2)) - 3| - 3)^2 - 2(2|((1(-1e^(-2x)) - 2)/(2(-1e^(-2x)) + 2)) - 3| - 3) - 5)^2 + 4(3(2|((1(-1e^(-2x)) - 2)/(2(-1e^(-2x)) + 2)) - 3| - 3)^2 - 2(2|((1(-1e^(-2x)) - 2)/(2(-1e^(-2x)) + 2)) - 3| - 3) - 5) + 2) + 4 = 0 have... | 7 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-4((-2(-1|(2|(1x^2 - 5x) - 1| + 3) - 3|) - 1)/(-2(-1|(2|(1x^2 - 5x) - 1| + 3) - 3|) + 3)) + 3) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(-3e^(1((-1(-2(1(1|x - 3| - 1)^2 - 2)^2 + 2(1(1|x - 3| - 1)^2 - 2) + 2) - 3)/(2(-2(1(1|x - 3| - 1)^2 - 2)^2 + 2(1(1|x - 3| - 1)^2 - 2) + 2) - 1)))) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role":... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(2π(-5(1((-1(-4((2x - 2)/(-3x + 4)) - 3) + 2)/(-3(-4((2x - 2)/(-3x + 4)) - 3) - 2))^2) + 5) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 548 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3((2((-2(2(4(-1x^2 + 4x + 5)^2 + 4(-1x^2 + 4x + 5) + 3)^2 - 5(4(-1x^2 + 4x + 5)^2 + 4(-1x^2 + 4x + 5) + 3) + 4) - 2)/(1(2(4(-1x^2 + 4x + 5)^2 + 4(-1x^2 + 4x + 5) + 3)^2 - 5(4(-1x^2 + 4x + 5)^2 + 4(-1x^2 + 4x + 5) + 3) + 4) - 3)) - 2)/(1((... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2|((-1(5(-1(-3x^2 + 1x + 2) - 4)^2 + 3(-1(-3x^2 + 1x + 2) - 4) - 5))/(-1(5(-1(-3x^2 + 1x + 2) - 4)^2 + 3(-1(-3x^2 + 1x + 2) - 4) - 5) - 3)) - 3| - 3) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 4 | MATH |
[
{
"content": "How many solutions does the equation 1(-1((-1(-1(1|(-2|x| - 3) + 3| - 3) + 2) + 1)/(2(-1(1|(-2|x| - 3) + 3| - 3) + 2) + 1)) + 3)^2 + 5(-1((-1(-1(1|(-2|x| - 3) + 3| - 3) + 2) + 1)/(2(-1(1|(-2|x| - 3) + 3| - 3) + 2) + 1)) + 3) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex forma... | 4 | MATH |
[
{
"content": "How many solutions does the equation -1sin(1π(-1(-3|((-3(3|(-2|x - 1| + 2)| + 3) - 3)/(-1(3|(-2|x - 1| + 2)| + 3) + 2)) + 2| - 3) - 1) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 47 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (2(-4(-1(-2sin(2π((2((3x - 3)/(-1x + 2)) + 3)/(1((3x - 3)/(-1x + 2)) + 1)) + 2)) + 1) + 4) - 2)/(-3(-4(-1(-2sin(2π((2((3x - 3)/(-1x + 2)) + 3)/(1((3x - 3)/(-1x + 2)) + 1)) + 2)) + 1) + 4)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex for... | 18 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(-2|(-3|(3(-5(2x^2 - 5x + 1)^2) + 5)| + 3) - 3| - 1)^2 + 4(-2|(-3|(3(-5(2x^2 - 5x + 1)^2) + 5)| + 3) - 3| - 1) - 3 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) = 4(5(-2((1(5((3x - 2)/(-3x - 3)) + 3) - 2)/(2(5((3x - 2)/(-3x - 3)) + 3) + 3))^2 + 3((1(5((3x - 2)/(-3x - 3)) + 3) - 2)/(2(5((3x - 2)/(-3x - 3)) + 3) + 3)) - 1) + 1)^2 + 4(5(-2((1(5((3x - 2)/(-3x - 3)) + 3) - 2)/(2(5((3x - 2)/(-3x - 3)) + 3... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2(-1|(1(4(-2(1x + 3)^2 + 5)^2 + 4(-2(1x + 3)^2 + 5) - 4)^2 + 2(4(-2(1x + 3)^2 + 5)^2 + 4(-2(1x + 3)^2 + 5) - 4) + 1) + 3| + 3) - 2)/(-2(-1|(1(4(-2(1x + 3)^2 + 5)^2 + 4(-2(1x + 3)^2 + 5) - 4)^2 + 2(4(-2(1x + 3)^2 + 5)^2 + 4(-2(1x + 3)^2 + 5) - 4) + 1) + 3| ... | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2((1((3(-5((-2((2x - 2)/(2x + 3)) + 1)/(2((2x - 2)/(2x + 3)) + 1))^2 - 1((-2((2x - 2)/(2x + 3)) + 1)/(2((2x - 2)/(2x + 3)) + 1)) + 5))/(-3(-5((-2((2x - 2)/(2x + 3)) + 1)/(2((2x - 2)/(2x + 3)) + 1))^2 - 1((-2((2x - 2)/(2x + 3)) + 1)/(2((2x... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(2cos(1π(4(-2|((1(-2|x + 3| + 1) - 1)/(2(-2|x + 3| + 1) - 3))| + 3) - 5) + 2) - 3) - 3 have in the interval [-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) = 3(2(2((-1((-3(-3|x - 1| + 1) + 1)/(1(-3|x - 1| + 1) + 2)) + 1)/(-3((-3(-3|x - 1| + 1) + 1)/(1(-3|x - 1| + 1) + 2)) + 1))^2 - 5((-1((-3(-3|x - 1| + 1) + 1)/(1(-3|x - 1| + 1) + 2)) + 1)/(-3((-3(-3|x - 1| + 1) + 1)/(1(-3|x - 1| + 1) + 2)) + 1... | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2((2(-4(2|(-5((-3x - 3)/(3x + 1)) - 5)| - 3)^2 + 2(2|(-5((-3x - 3)/(3x + 1)) - 5)| - 3) + 3) - 1)/(-3(-4(2|(-5((-3x - 3)/(3x + 1)) - 5)| - 3)^2 + 2(2|(-5((-3x - 3)/(3x + 1)) - 5)| - 3) + 3) + 2)) - 3)/(-1((2(-4(2|(-5((-3x - 3)/(3x + 1)) - 5)... | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(3cos(3π(1(2((1(-2|x| + 3) + 3)/(-2(-2|x| + 3) + 3)) + 1) + 4) + 1)) - 2| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "How many solutions does the equation 2cos(3π(3(3|((-2(-2(-2|x + 2| - 3)^2 + 2(-2|x + 2| - 3) + 5) + 3)/(2(-2(-2|x + 2| - 3)^2 + 2(-2|x + 2| - 3) + 5) + 2))| - 3) + 1) - 2) - 1 = 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) = 3(3(-3|(-1|(-1|(-1|x + 1|) - 2| + 3) + 3| + 1) + 2| + 2) + 5)^2 - 3(3(-3|(-1|(-1|(-1|x + 1|) - 2| + 3) + 3| + 1) + 2| + 2) + 5) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12 | MATH |
[
{
"content": "How many solutions does the equation -1(-5(3sin(2π(-2|(1((2x + 3)/(3x - 1))^2 + 5((2x + 3)/(3x - 1)) + 2) - 1|)) + 1) - 1)^2 + 3(-5(3sin(2π(-2|(1((2x + 3)/(3x - 1))^2 + 5((2x + 3)/(3x - 1)) + 2) - 1|)) + 1) - 1) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Yo... | 174 | MATH |
[
{
"content": "How many solutions does the equation -3(2|(2|(1(-1(4x^2 - 4x - 3)^2 + 3(4x^2 - 4x - 3) + 4) + 3) + 3| - 3) - 3|)^2 - 2(2|(2|(1(-1(4x^2 - 4x - 3)^2 + 3(4x^2 - 4x - 3) + 4) + 3) + 3| - 3) - 3|) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"ro... | 14 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(5(-3sin(3π(-3((1(-4x^2 - 1x) + 2)/(-1(-4x^2 - 1x) - 1))^2 - 5((1(-4x^2 - 1x) + 2)/(-1(-4x^2 - 1x) - 1)) - 2) - 2)) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 96 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(2(-3(-5(-4(-4x - 3) + 3)^2 + 5))^2 + 4(-3(-5(-4(-4x - 3) + 3)^2 + 5))) - 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation (2(-4(4(-2|(-3(3|x - 2| - 2)^2 - 1) + 3| + 1) - 4)^2 - 2(4(-2|(-3(3|x - 2| - 2)^2 - 1) + 3| + 1) - 4) - 1) + 2)/(-2(-4(4(-2|(-3(3|x - 2| - 2)^2 - 1) + 3| + 1) - 4)^2 - 2(4(-2|(-3(3|x - 2| - 2)^2 - 1) + 3| + 1) - 4) - 1) - 1) = 0 have in the range [-10, 10]?\n\n... | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|(-3(-2|(-4(1(-3x + 2)^2 + 3(-3x + 2) + 1)^2 - 3(1(-3x + 2)^2 + 3(-3x + 2) + 1) + 2) + 1| + 3)^2 - 4(-2|(-4(1(-3x + 2)^2 + 3(-3x + 2) + 1)^2 - 3(1(-3x + 2)^2 + 3(-3x + 2) + 1) + 2) + 1| + 3) - 4) + 3| + 3 where -10 ≤ x ≤ 10.\n\nPresent the a... | 12 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2(1((1(1sin(3π(-5(1x^2 + 1x + 2)^2 - 5(1x^2 + 1x + 2)) - 1)) + 3)/(3(1sin(3π(-5(1x^2 + 1x + 2)^2 - 5(1x^2 + 1x + 2)) - 1))))^2 + 5((1(1sin(3π(-5(1x^2 + 1x + 2)^2 - 5(1x^2 + 1x + 2)) - 1)) + 3)/(3(1sin(3π(-5(1x^2 + 1x + 2)^2 - 5(1x^2 + 1x + 2... | 40 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1(2e^(-2(3|(-5(1|(2|x - 2| - 1) - 3| - 3)^2 + 4(1|(2|x - 2| - 1) - 3| - 3) + 2) + 3| - 1)) + 1)^2 - 2(2e^(-2(3|(-5(1|(2|x - 2| - 1) - 3| - 3)^2 + 4(1|(2|x - 2| - 1) - 3| - 3) + 2) + 3| - 1)) + 1) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer i... | 12 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-2cos(1π(-2|(3(2|(-1x - 1) - 1| + 2) + 3) - 1| + 2)) - 1) + 2)/(-3(-2cos(1π(-2|(3(2|(-1x - 1) - 1| + 2) + 3) - 1| + 2)) - 1) + 4) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "How many solutions does the equation -1(-2(-5(-2|(5((-2x)/(1x + 3)) - 2) + 2| + 1)^2 - 5(-2|(5((-2x)/(1x + 3)) - 2) + 2| + 1) - 1) + 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 solutions does the equation 1(-3(-1|(-3|((-3(3|x| - 3) - 2)/(-3(3|x| - 3) + 4)) + 3| + 1) + 2|)^2 - 2(-1|(-3|((-3(3|x| - 3) - 2)/(-3(3|x| - 3) + 4)) + 3| + 1) + 2|) + 3)^2 + 4(-3(-1|(-3|((-3(3|x| - 3) - 2)/(-3(3|x| - 3) + 4)) + 3| + 1) + 2|)^2 - 2(-1|(-3|((-3(3|x| - 3) - 2)/(-3(3|x| - 3) ... | 12 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1e^(-2(3|(5(-1|(3|((1x - 1)/(2x + 3)) + 3| + 1) - 3| + 2)^2 + 2(-1|(3|((1x - 1)/(2x + 3)) + 3| + 1) - 3| + 2) - 5) - 1| - 2)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-3|(-1|(1|((3(-1x^2 - 4x + 3))/(-3(-1x^2 - 4x + 3) + 2)) - 3| + 1) + 3| + 2)| + 2) + 3| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 1((-2(1(1(-3((-1x - 1)/(3x - 2))^2 - 5((-1x - 1)/(3x - 2)) - 3) - 3) + 4) - 3)/(-2(1(1(-3((-1x - 1)/(3x - 2))^2 - 5((-1x - 1)/(3x - 2)) - 3) - 3) + 4) - 2))^2 + 5((-2(1(1(-3((-1x - 1)/(3x - 2))^2 - 5((-1x - 1)/(3x - 2)) - 3) - 3) + 4) - 3)/(-2(1(1(-3((-1x - 1)/... | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-3(-3(-3cos(2π((2((1x + 3)/(3x - 2)))/(-2((1x + 3)/(3x - 2)) - 1)) + 1) - 1) + 5)^2 - 1(-3(-3cos(2π((2((1x + 3)/(3x - 2)))/(-2((1x + 3)/(3x - 2)) - 1)) + 1) - 1) + 5) + 2)^2 + 2(-3(-3(-3cos(2π((2((1x + 3)/(3x - 2)))/(-2((1x + 3)/(3x - 2)) - 1)) + 1) - 1) +... | 35 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-1((-2(4(1cos(3π((2(4x + 4) + 1)/(-1(4x + 4) - 2)) - 1) + 2)^2 - 4(1cos(3π((2(4x + 4) + 1)/(-1(4x + 4) - 2)) - 1) + 2) - 5) + 1)/(-1(4(1cos(3π((2(4x + 4) + 1)/(-1(4x + 4) - 2)) - 1) + 2)^2 - 4(1cos(3π((2(4x + 4) + 1)/(-1(4x + 4) - 2)) - 1... | 19 | MATH |
[
{
"content": "How many solutions does the equation -1sin(1π(1|(1|(1(4((-2x + 2)/(1x - 2)) + 5) - 2) - 1| - 1) + 1| + 1) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(3|((-2(-5((1(-3sin(1πx + 3) - 2) - 1)/(-1(-3sin(1πx + 3) - 2) + 2)) - 5) + 1)/(-1(-5((1(-3sin(1πx + 3) - 2) - 1)/(-1(-3sin(1πx + 3) - 2) + 2)) - 5) + 3))| - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 20 | MATH |
[
{
"content": "How many solutions does the equation (-2(3|((1((2(-1sin(3π(3x - 4) - 3)) + 2)/(3(-1sin(3π(3x - 4) - 3)) - 2)) - 1)/(1((2(-1sin(3π(3x - 4) - 3)) + 2)/(3(-1sin(3π(3x - 4) - 3)) - 2)) + 1)) - 1| - 3))/(2(3|((1((2(-1sin(3π(3x - 4) - 3)) + 2)/(3(-1sin(3π(3x - 4) - 3)) - 2)) - 1)/(1((2(-1sin(3π(3x - 4) ... | 180 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-2(-2e^(-2(-2|(-3|(4x + 1) + 2| + 1) + 2| + 3)) + 3)^2 - 1(-2e^(-2(-2|(-3|(4x + 1) + 2| + 1) + 2| + 3)) + 3) + 4) - 3 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(-1cos(2π(3(-3|(-4(1x^2 - 5x + 3)^2 + 4(1x^2 - 5x + 3) + 2) + 1| - 3) - 2) + 1) - 1) - 1)/(1(-1cos(2π(3(-3|(-4(1x^2 - 5x + 3)^2 + 4(1x^2 - 5x + 3) + 2) + 1| - 3) - 2) + 1) - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxe... | 909 | MATH |
[
{
"content": "How many solutions does the equation -2(2|(2(-1|(5(-2|x - 2| + 1) - 5) - 1| - 1) + 5) + 2| - 1)^2 + 5(2|(2(-1|(5(-2|x - 2| + 1) - 5) - 1| - 1) + 5) + 2| - 1) + 5 = 0 have in the range [-10, 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) = -2cos(2π(4((-1(-2(-2(2|x + 2| - 1) - 4)^2 - 4(-2(2|x + 2| - 1) - 4) + 3) - 1)/(-2(-2(-2(2|x + 2| - 1) - 4)^2 - 4(-2(2|x + 2| - 1) - 4) + 3) - 1)) + 4) + 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
... | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|((2((-3((1(-2(-1x^2 - 4x + 5) + 1) - 1)/(1(-2(-1x^2 - 4x + 5) + 1) - 2)) - 1)/(3((1(-2(-1x^2 - 4x + 5) + 1) - 1)/(1(-2(-1x^2 - 4x + 5) + 1) - 2)) + 3)) - 2)/(-1((-3((1(-2(-1x^2 - 4x + 5) + 1) - 1)/(1(-2(-1x^2 - 4x + 5) + 1) - 2)) - 1)/(3... | 4 | MATH |
[
{
"content": "How many solutions does the equation 4((-2(-1(1(3|(-5x + 5) + 3| - 3) - 4)^2 - 1(1(3|(-5x + 5) + 3| - 3) - 4)) + 1)/(3(-1(1(3|(-5x + 5) + 3| - 3) - 4)^2 - 1(1(3|(-5x + 5) + 3| - 3) - 4)) + 3))^2 + 1((-2(-1(1(3|(-5x + 5) + 3| - 3) - 4)^2 - 1(1(3|(-5x + 5) + 3| - 3) - 4)) + 1)/(3(-1(1(3|(-5x + 5) + ... | 4 | MATH |
[
{
"content": "How many solutions does the equation 2(1(-1|(-3(-1|(-3x + 1) + 2| + 2) - 5) - 1| + 3)^2 + 4(-1|(-3(-1|(-3x + 1) + 2| + 2) - 5) - 1| + 3) + 4) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
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