instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What is -15602 (base 11) in base 14?\n | -8052\n | ibivibiv/math_instruct | |
Simplify (6*(-1*sqrt(1872) + sqrt(1872) - sqrt(1872))/sqrt(4) - (3 + sqrt(13) + 5 + (sqrt(156)*3)/sqrt(12))**2)*-5.\n | 1360 + 500*sqrt(13)\n | ibivibiv/math_instruct | |
Let c = 121 + -27. Suppose 5*g = -c - 31. Let h = -27 - g. What is the nearest to 0.4 in h, -1/2, -1?\n | -1/2\n | ibivibiv/math_instruct | |
Let x(z) = 10040*z + 9. Let l be x(5). Let p = l + -27579. Let w = p - -144370. Round w to the nearest 10000.\n | 170000\n | ibivibiv/math_instruct | |
What is ((-36)/(-42))/(10/30*3/(-42))?\n | -36\n | ibivibiv/math_instruct | |
In Marias desk drawer, there are 8 red pens, twice as many black pens as red pens, and 5 more blue pens than black pens. Additionally, there are half as many green pens as blue pens, and the number of purple pens is the same as the difference between the number of red pens and green pens. How many pens are there in all... | Let's calculate the number of each color of pens step by step:
1. Red pens: There are 8 red pens.
2. Black pens: There are twice as many black pens as red pens, so:
Black pens = 2 * Red pens = 2 * 8 = 16 black pens.
3. Blue pens: There are 5 more blue pens than black pens, so:
Blue pens = Black pens + 5 = 16 +... | ibivibiv/math_instruct | |
Let x(w) be the first derivative of -23*w**7/210 + w**5/4 - 4*w**2 + 16. Let s(f) be the second derivative of x(f). What is the third derivative of s(m) wrt m?\n | -552*m\n | ibivibiv/math_instruct | |
Let l(g) = -374*g**3 - g**2 - 7*g + 23. Is l(-4) prime?\n | True\n | ibivibiv/math_instruct | |
Let i(z) = 3*z**3 + 4*z**2 + 4*z - 4. Let a(t) = 15*t**3 + 21*t**2 + 21*t - 21. Let f be 259/14 - 10/(-4). Suppose -5*o - 3 - 17 = 0. What is f*i(w) + o*a(w)?\n | 3*w**3\n | ibivibiv/math_instruct | |
Suppose -12*r - 235 = -7*r. Let m = -45 - r. What is the lowest common multiple of 4 and m?\n | 4\n | ibivibiv/math_instruct | |
In base 3, what is -10220211021020 + 102?\n | -10220211020211\n | ibivibiv/math_instruct | |
Solve -h + 3*y - 12 = 0, 8*h + 2*y = 12*h - 2 for h.\n | 3\n | ibivibiv/math_instruct | |
3 + 203917462\n | 203917465\n | ibivibiv/math_instruct | |
Find the second derivative of 29235475*x**3 + 20278065*x.\n | 175412850*x\n | ibivibiv/math_instruct | |
Evaluate -1*((-15266)/(-4939))/(-1*(-32)/44).\n | -17/4\n | ibivibiv/math_instruct | |
Is 48 a factor of 11412?\n | False\n | ibivibiv/math_instruct | |
Total of -11025.68 and 2.\n | -11023.68\n | ibivibiv/math_instruct | |
Three letters picked without replacement from daqatauatttt. What is prob of sequence tda?\n | 1/66\n | ibivibiv/math_instruct | |
What are the prime factors of 5294?\n | 2, 2647\n | ibivibiv/math_instruct | |
Simplify sqrt(24)/(2*sqrt(432) + sqrt(432)).\n | sqrt(2)/18\n | ibivibiv/math_instruct | |
Calculate prob of sequence jyj when three letters picked without replacement from {j: 3, e: 3, r: 1, p: 2, y: 1}.\n | 1/120\n | ibivibiv/math_instruct | |
What is the second derivative of -b*l**3 - 4*b*l**2 - 43182*b*l + 2*l**5 + 4*l**3 - 2*l wrt l?\n | -6*b*l - 8*b + 40*l**3 + 24*l\n | ibivibiv/math_instruct | |
Which is the fifth smallest value? (a) -3 (b) -5 (c) -27 (d) 0.3 (e) -1/267 (f) 5\n | d\n | ibivibiv/math_instruct | |
Suppose 9*q = 14 - 23. List the prime factors of -2 - (41*q)/(5/80).\n | 2, 3, 109\n | ibivibiv/math_instruct | |
Let u(o) = -21*o**3 - 2*o - 1. Let w be u(-1). Let f(y) = -2*y**2 - 12 + w*y + 10*y**2 - 7*y. Is f(13) a composite number?\n | True\n | ibivibiv/math_instruct | |
What is the value of (-16 - (21 - 44)) + (0 - -4) + -16 + 2?\n | -3\n | ibivibiv/math_instruct | |
What is the next term in -1887, -3795, -5701, -7605?\n | -9507\n | ibivibiv/math_instruct | |
b"What is the ith term of -147079289, -294158578, -441237867, -588317156?\n" | -147079289*i\n | ibivibiv/math_instruct | |
Simplify 4 + sqrt(25)/(sqrt(500)*-6 - sqrt(5)).\n | -sqrt(5)/61 + 4\n | ibivibiv/math_instruct | |
Which is the nearest to -1? (a) 4 (b) 17 (c) 1\n | c\n | ibivibiv/math_instruct | |
Divide 17688 by -4.\n | -4422\n | ibivibiv/math_instruct | |
Let g = -4077 - -4076. What is the nearest to g in 4, -1, 0, 2/33?\n | -1\n | ibivibiv/math_instruct | |
Let a(u) = 7*u**2 - 17*u - 5. Let g be (87/(-87))/((-1)/(-2)). Let l(i) = -3*i**2 + 8*i + 2. Calculate g*a(z) - 5*l(z).\n | z**2 - 6*z\n | ibivibiv/math_instruct | |
Let l(c) be the first derivative of -25*c**2/2 - 78*c + 37. Differentiate l(n) wrt n.\n | -25\n | ibivibiv/math_instruct | |
Put -0.04, -57, 11, 3.1 in decreasing order.\n | 11, 3.1, -0.04, -57\n | ibivibiv/math_instruct | |
What is the cube root of 19117 to the nearest integer?\n | 27\n | ibivibiv/math_instruct | |
List the prime factors of 1860131.\n | 7, 13, 20441\n | ibivibiv/math_instruct | |
Which is the nearest to -2/5? (a) -2/11 (b) 41 (c) -0.2 (d) 6/29\n | c\n | ibivibiv/math_instruct | |
What is -0.0000424724 rounded to 7 decimal places?\n | -0.0000425\n | ibivibiv/math_instruct | |
Is 107419 prime?\n | False\n | ibivibiv/math_instruct | |
Let o(g) = 4*g + 75. Let c(s) = s + 15. Let v(l) = 5*c(l) - o(l). Let z(y) = 14*y. What is v(z(h))?\n | 14*h\n | ibivibiv/math_instruct | |
What is ((-3)/(-164))/((-18)/288*-6)?\n | 2/41\n | ibivibiv/math_instruct | |
Suppose 3*m = -2*l + 1, -7*l + 2*l + 3*m + 13 = 0. Let g be 0 + l/2 + 0. Suppose -g + 17 = y - b, -b = y - 6. What is the remainder when 31 is divided by y?\n | 9\n | ibivibiv/math_instruct | |
Let w(v) = -v**3 + 7*v**2 - 7*v - 1. Calculate the remainder when 55 is divided by w(5).\n | 13\n | ibivibiv/math_instruct | |
What are the prime factors of 722142?\n | 2, 3, 43, 311\n | ibivibiv/math_instruct | |
Which is the fourth biggest value? (a) 8.7 (b) 0.2 (c) 1/3 (d) -8 (e) -4\n | e\n | ibivibiv/math_instruct | |
-618 (base 15) to base 12\n | -965\n | ibivibiv/math_instruct | |
Let u = 0.101 - -8.699. Let f = u + -0.8. Let w = f + -7.972. What is w rounded to 2 dps?\n | 0.03\n | ibivibiv/math_instruct | |
Solve 0 = -3*n + 2*z - 95, -1049*z = 5*n - 908*z - 419 for n.\n | -29\n | ibivibiv/math_instruct | |
Which is the closest to 0? (a) -6 (b) 8/5 (c) 0 (d) 4/5\n | c\n | ibivibiv/math_instruct | |
Let i(n) = 5*n**2 - 240*n + 2. Let g(y) = -6*y**2 + 243*y - 3. Calculate -6*g(w) - 7*i(w).\n | w**2 + 222*w + 4\n | ibivibiv/math_instruct | |
Suppose 4*n + 5 = -3. Let u = -9 - -8. Sort u, -5, n in ascending order.\n | -5, n, u\n | ibivibiv/math_instruct | |
What is the first derivative of -186120*f**2 + 42*f + 16080916?\n | -372240*f + 42\n | ibivibiv/math_instruct | |
How many minutes are there between 12:04 AM and 9:53 AM?\n | 589\n | ibivibiv/math_instruct | |
Let k(p) be the second derivative of -2*p**3/3 + p**2/2 - 27*p. Let v be (-2)/(-3) - (-8)/6. What is k(v)?\n | -7\n | ibivibiv/math_instruct | |
Is 46923295 a multiple of 619?\n | True\n | ibivibiv/math_instruct | |
Factor 46/7*y + 2/7*y**3 - 18/7*y**2 - 30/7.\n | 2*(y - 5)*(y - 3)*(y - 1)/7\n | ibivibiv/math_instruct | |
In base 14, what is 1738 + 6?\n | 1740\n | ibivibiv/math_instruct | |
Let i(t) be the second derivative of t**7/6300 - t**6/600 + t**5/150 - t**4/4 - 2*t. Let s(q) be the third derivative of i(q). What is c in s(c) = 0?\n | 1, 2\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# The geometry behind the lemniscatic integral: $u' = \int^t_0(4t(1-t^2))^{-1/2}\,dt$
From a translated version of this (page 111):
One can easily recognise that in this case, the lemniscatic integral $$u' = \int^t_0\frac{d... | We will delve into the concept of conformal mappings and how they relate to the lemniscatic integral, particularly in the context of transforming half-planes onto a square. To begin, let us establish a clear definition of conformal mappings.
A function f(z) between two complex domains is said to be conformal at a poi... | ibivibiv/math_instruct | |
Let g = -0.1 - 0. Let p = 10 + 30. Let j be ((-30)/p)/(3/2). What is the nearest to -1 in g, j, -3?\n | j\n | ibivibiv/math_instruct | |
Solve 8*w - 775 = -354 - 333 for w.\n | 11\n | ibivibiv/math_instruct | |
Solve 30872*m - 30873*m + 4*n = -13, 41 = 5*m + 4*n for m.\n | 9\n | ibivibiv/math_instruct | |
Find the first derivative of 5709*j*z**2 - 2*j*z - j - 8*z**2 + 2121549 wrt z.\n | 11418*j*z - 2*j - 16*z\n | ibivibiv/math_instruct | |
What is the value of (1 - 4)*8618/(-834)?\n | 31\n | ibivibiv/math_instruct | |
Two letters picked without replacement from weikwooerioe. What is prob of sequence or?\n | 1/44\n | ibivibiv/math_instruct | |
Suppose -4*u - 498 = -3*j - 1541, 5*u - 1296 = -4*j. What is the hundreds digit of u?\n | 2\n | ibivibiv/math_instruct | |
Solve -2*j - 7 = -d, 8*j + 10 = 3*j for d.\n | 3\n | ibivibiv/math_instruct | |
Which is the biggest value? (a) 79 (b) 10 (c) -53 (d) 0.8 (e) 0.16\n | a\n | ibivibiv/math_instruct | |
What is the thousands digit of 78112?\n | 8\n | ibivibiv/math_instruct | |
Do 2965 and 2966 have the same value?\n | False\n | ibivibiv/math_instruct | |
Let z(k) = -9*k**2 + 13 + 2*k - 3*k + k**3 - 3*k + 3*k. Let l be z(9). Suppose -x + 0 = -l. What is the greatest common divisor of x and 6?\n | 2\n | ibivibiv/math_instruct | |
Let t(q) = -3*q**3 + 6*q**2 - 9. Let x(b) be the second derivative of -b**5/10 + b**4/4 - 5*b**2/2 - b. Calculate 3*t(s) - 5*x(s).\n | s**3 + 3*s**2 - 2\n | ibivibiv/math_instruct | |
Daniel collects Russian dolls that normally cost $4 each. He saves enough money to buy 15 Russian dolls. However, the price suddenly drops to $3 each. How many Russian dolls can he buy now at the discounted price, given his savings? | With the price of each doll at $4, this means he has saved a total of 15 * 4 = $60.
When the price is lowered to $3 each, he can now purchase 60 / 3 = 20 dolls.
The answer is 20 | ibivibiv/math_instruct | |
Suppose 0 = 5*r + 5*k - 100, r - 14 = 5*k - 6. List the prime factors of (12/(-10))/(r/(-2565)).\n | 3, 19\n | ibivibiv/math_instruct | |
Four letters picked without replacement from {b: 1, n: 4, f: 2, r: 1}. What is prob of sequence fnbf?\n | 1/210\n | ibivibiv/math_instruct | |
Let f(a) = 8*a**3 - 19*a**2 + 4*a + 25. Let n(u) = -22*u**3 + 57*u**2 - 11*u - 72. Let s(z) = 17*f(z) + 6*n(z). Calculate s(-5).\n | -42\n | ibivibiv/math_instruct | |
41 (base 10) to base 13\n | 32\n | ibivibiv/math_instruct | |
What is the common denominator of 30/23119 and 79/2?\n | 46238\n | ibivibiv/math_instruct | |
Suppose 1222*u = 1226*u - 9004. Does u = 2251?\n | True\n | ibivibiv/math_instruct | |
Let y = 0.3 + -0.1. Let b = y - 0.1. Let a = 0.4 + 2.6. Put a, -0.1, b in descending order.\n | a, b, -0.1\n | ibivibiv/math_instruct | |
Factor -4*q**2 - 3172*q + 12752.\n | -4*(q - 4)*(q + 797)\n | ibivibiv/math_instruct | |
Suppose -38 = -15*c + 1567. What is the remainder when c is divided by 6?\n | 5\n | ibivibiv/math_instruct | |
Let o = 355 - 355. Suppose -7*l - 24 + 45 = o. Solve -21 = 8*w + l for w.\n | -3\n | ibivibiv/math_instruct | |
What is 142679885 to the power of 1/2, to the nearest integer?\n | 11945\n | ibivibiv/math_instruct | |
How many months are there in seven sixteenths of a millennium?\n | 5250\n | ibivibiv/math_instruct | |
What comes next: -4736, -9520, -14304?\n | -19088\n | ibivibiv/math_instruct | |
What is 0.000006486378 rounded to seven dps?\n | 0.0000065\n | ibivibiv/math_instruct | |
How many minutes are there between 5:29 AM and 1:30 PM?\n | 481\n | ibivibiv/math_instruct | |
Let s(m) = 5*m - 16. Let t be s(5). Suppose 0 = 8*r - 5*r - t. List the prime factors of r.\n | 3\n | ibivibiv/math_instruct | |
Let j be 15*(2 - 1)*(-6)/(-9). Let d be 16/8*(12 - j). Solve -196/9*t**d + 868/9*t**3 - 368/9*t - 64/9 - 80/3*t**2 = 0.\n | -2/7, 1, 4\n | ibivibiv/math_instruct | |
Let h(v) = 82*v - 2980. Is 22 a factor of h(68)?\n | True\n | ibivibiv/math_instruct | |
What is the second derivative of -5*i**3 + 700*i**2 - 1476*i - 521*i**2 - 2*i**4 + 4*i**3 - 389*i**2 wrt i?\n | -24*i**2 - 6*i - 420\n | ibivibiv/math_instruct | |
Let q(i) = -65*i - 11. Let w be q(-2). What is the greatest common divisor of 35 and w?\n | 7\n | ibivibiv/math_instruct | |
Suppose -3*h - 4*y = 6 - 117, 0 = -3*y. What are the prime factors of h?\n | 37\n | ibivibiv/math_instruct | |
Suppose -36 = 2*h - 8*h. Suppose 5*d + 16 = h*d. What are the prime factors of d?\n | 2\n | ibivibiv/math_instruct | |
Let q(h) be the third derivative of -h**9/504 - 2*h**7/35 + 2*h**6/15 - 11*h**5/6 - h**4/6 - 2831*h**2 - 2. Find the third derivative of q(z) wrt z.\n | -120*z**3 - 288*z + 96\n | ibivibiv/math_instruct | |
Let s(u) = -4*u**2 + 2. Let r(y) be the first derivative of -y**5/120 + 3*y**3 + 15. Let c(m) be the third derivative of r(m). Calculate s(c(b)).\n | -4*b**2 + 2\n | ibivibiv/math_instruct | |
Simplify ((u*u/u**19*u)/u)/u*u*u**(-7/2) assuming u is positive.\n | u**(-41/2)\n | ibivibiv/math_instruct | |
What are the prime factors of 362638?\n | 2, 31, 5849\n | ibivibiv/math_instruct |
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