instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What is the hundreds digit of 276371192?\n | 1\n | ibivibiv/math_instruct | |
Simplify -1*((sqrt(605) - -1*(1 + sqrt(605))) + -3 + 0 + sqrt(605) + -3)**2 + 3 + 1 + -3.\n | -5469 + 330*sqrt(5)\n | ibivibiv/math_instruct | |
Collect the terms in 15*a + 10*a - 27*a + 4*a**3.\n | 4*a**3 - 2*a\n | ibivibiv/math_instruct | |
Expand (-1 - 3*m + 1)*(2 - 2 - m)*(218*m - 37*m + 62*m).\n | 729*m**3\n | ibivibiv/math_instruct | |
In base 10, what is 23614 + -5?\n | 23609\n | ibivibiv/math_instruct | |
Let z = -10 - -31/3. Let t = -0.47 - 3.53. Sort t, 4, z in ascending order.\n | t, z, 4\n | ibivibiv/math_instruct | |
Solve 2*i + 8 = 0, d - 4*i + 7181 - 7192 = 2*d for d.\n | 5\n | ibivibiv/math_instruct | |
Suppose 40*x = 32*x + 864. Find the third derivative of x*d**2 + 20*d**3 - 27*d - 111*d**2 + 17*d wrt d.\n | 120\n | ibivibiv/math_instruct | |
What comes next: 8417564, 16835133, 25252706, 33670283?\n | 42087864\n | ibivibiv/math_instruct | |
Let f = -86 + 241. What are the prime factors of f?\n | 5, 31\n | ibivibiv/math_instruct | |
Collect the terms in -908*d**2 + 2749*d**2 + 6*d**3 - 922*d**2 - 919*d**2.\n | 6*d**3\n | ibivibiv/math_instruct | |
Let f(w) = -w**3 + 5*w**2 + 5*w + 13. Suppose -83 + 19 = -2*y. Let g be ((-27)/12)/((-12)/y). Calculate the remainder when 22 is divided by f(g).\n | 1\n | ibivibiv/math_instruct | |
Let j(r) be the first derivative of -5*r + 11/4*r**4 - 7/3*r**3 + 0*r**2 + 0*r**5 - 68 + 1/2*r**6. Find the third derivative of j(k) wrt k.\n | 180*k**2 + 66\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# For every partition $\pi$ of a fixed integer $n$, $\sum{F(\pi)}=\sum{G(\pi)}$
I need to prove the following question.
For every partition $\pi$ of a fixed integer $n$, define $F(\pi)$=number of occurrences of 1 as a summa... | To begin, let us clarify the definitions of the terms used in the statement of the problem. A partition of a positive integer n is a way to express n as a sum of positive integers, where the order of the summands does not matter. We denote a partition of n as π, and we often represent partitions using Young diagrams, ... | ibivibiv/math_instruct | |
Put -7, 1/552, -4, -2/19, 5, 2486 in ascending order.\n | -7, -4, -2/19, 1/552, 5, 2486\n | ibivibiv/math_instruct | |
What is -46 divided by 2807?\n | -46/2807\n | ibivibiv/math_instruct | |
Let -6*k**5/11 - 32*k**4/11 + 30*k**3/11 + 32*k**2/11 - 24*k/11 = 0. What is k?\n | -6, -1, 0, 2/3, 1\n | ibivibiv/math_instruct | |
Calculate 201 divided by 101.\n | 201/101\n | ibivibiv/math_instruct | |
Let k = 0.134 + -6.234. Let c = 17.5 - k. Round c to the nearest 10.\n | 20\n | ibivibiv/math_instruct | |
Let m be -1*6/(-35)*5. Let o = -2 + 6. Let p be 3*(-1)/(-12)*(-46 - 14)/(-15). What is the closest to p in o, -0.2, m?\n | m\n | ibivibiv/math_instruct | |
Let g(o) = -4*o**2 + 9685*o + 383752. Give g(-39).\n | -47\n | ibivibiv/math_instruct | |
Let x be (-25)/35*2/(-5). Let a = -104 + 104.5. What is the nearest to x in 4, -5, a?\n | a\n | ibivibiv/math_instruct | |
Let g(d) = -143*d - 284. Let t be g(-2). Suppose -4*k = -7*k - 165. Let f be 424/((t - 1) + 44/k). Round f to the nearest 100.\n | 2100\n | ibivibiv/math_instruct | |
What is the value of (-80)/(-300)*2/8*2?\n | 2/15\n | ibivibiv/math_instruct | |
List the prime factors of 6902.\n | 2, 7, 17, 29\n | ibivibiv/math_instruct | |
Let a = -1120 - -1756. List the prime factors of a.\n | 2, 3, 53\n | ibivibiv/math_instruct | |
Suppose -5*k - 2*k + 14 = 0. Let t(r) = -9*r**2 + 26*r**2 - 4*r - 3*r**2 - 11*r**2 - k. What is the units digit of t(-5)?\n | 3\n | ibivibiv/math_instruct | |
Is -31 at most -475/16?\n | True\n | ibivibiv/math_instruct | |
Let w(f) = -f**2 + 28*f - 47. Let p be w(2). Suppose 1 = 5*v - 9. What is the highest common divisor of v and p?\n | 1\n | ibivibiv/math_instruct | |
Four letters picked without replacement from pppppppwpwp. Give prob of sequence wppp.\n | 7/55\n | ibivibiv/math_instruct | |
Simplify 4*(sqrt(176) + 1) + (0 + sqrt(1331) - sqrt(11)*2*-3) + 5.\n | 9 + 33*sqrt(11)\n | ibivibiv/math_instruct | |
Let v(p) = 34*p + 8 - 8 - 9*p. Let r(n) = 2*n + 40. Let w(j) = -j - 15. Let i(q) = -3*r(q) - 8*w(q). What is i(v(o))?\n | 50*o\n | ibivibiv/math_instruct | |
Sort 57, 5, -93, -3670.\n | -3670, -93, 5, 57\n | ibivibiv/math_instruct | |
What comes next: 1450, 2898, 4346, 5794, 7242?\n | 8690\n | ibivibiv/math_instruct | |
What is prob of picking 3 g and 1 p when four letters picked without replacement from ggggpgp?\n | 4/7\n | ibivibiv/math_instruct | |
Let q(s) = -s**2 - 8*s - 7. Let r be q(-3). What are the prime factors of 3/(2 - 14) + 402/r?\n | 2, 5\n | ibivibiv/math_instruct | |
Three letters picked without replacement from irlrrriiririiirlrlil. Give prob of picking 3 i.\n | 14/285\n | ibivibiv/math_instruct | |
Calculate the remainder when 77661 is divided by 225.\n | 36\n | ibivibiv/math_instruct | |
Let l = -437237 - -1088237. What is l rounded to the nearest 1000000?\n | 1000000\n | ibivibiv/math_instruct | |
Collect the terms in 15*a**3 + 1621872*a - 3249424*a + 1627552*a.\n | 15*a**3\n | ibivibiv/math_instruct | |
Round 66.75594 to zero dps.\n | 67\n | ibivibiv/math_instruct | |
What is the hundreds digit of 78394?\n | 3\n | ibivibiv/math_instruct | |
Is 78786247 composite?\n | True\n | ibivibiv/math_instruct | |
Let o = -53573150.999967 - -53573227. Let l = o + -76. Round l to 5 dps.\n | 0.00003\n | ibivibiv/math_instruct | |
Multiply -358 and -2.\n | 716\n | ibivibiv/math_instruct | |
What is prob of sequence eda when three letters picked without replacement from {d: 1, a: 1, b: 1, e: 2}?\n | 1/30\n | ibivibiv/math_instruct | |
Solve 0 = -108028*h + 108004*h - 192 for h.\n | -8\n | ibivibiv/math_instruct | |
Let j be 1*((-50)/4)/5*(-34)/(-170)*-4. Let d = 1 + -1. Solve d = j*z - 85 + 79 for z.\n | 3\n | ibivibiv/math_instruct | |
Let b = 89.7 + -169.1. What is b rounded to the nearest ten?\n | -80\n | ibivibiv/math_instruct | |
Product of 1084704663 and 0.5.\n | 542352331.5\n | ibivibiv/math_instruct | |
Put 3, -3, 10 in increasing order.\n | -3, 3, 10\n | ibivibiv/math_instruct | |
What is 2435 divided by -487?\n | -5\n | ibivibiv/math_instruct | |
Two letters picked without replacement from sstsststssssssssst. Give prob of picking 1 s and 1 t.\n | 56/153\n | ibivibiv/math_instruct | |
What is the seventh root of 8927 to the nearest integer?\n | 4\n | ibivibiv/math_instruct | |
Let h(d) = -115*d**3 - 7*d**2 - 7*d + 7. Let o(i) = 58*i**3 + 3*i**2 + 3*i - 3. Give 3*h(c) + 7*o(c).\n | 61*c**3\n | ibivibiv/math_instruct | |
Four letters picked without replacement from pqqpfpyyffpfypqpptf. Give prob of picking 1 t, 1 q, and 2 y.\n | 3/1292\n | ibivibiv/math_instruct | |
Three letters picked without replacement from fgvgvhggfgvvmhgvfvm. What is prob of sequence ghg?\n | 10/969\n | ibivibiv/math_instruct | |
Let c(f) = 2*f**2 - 2*f + 1. Let x(p) = -10*p**2 + 10*p - 5. Give 11*c(a) + 2*x(a).\n | 2*a**2 - 2*a + 1\n | ibivibiv/math_instruct | |
Let k(f) = -f**4 - 138*f**3 - 484*f**2 + 4*f - 6. Let q(i) = -3*i**4 - 689*i**3 - 2422*i**2 + 22*i - 33. Let j(m) = 11*k(m) - 2*q(m). Factor j(n).\n | -5*n**2*(n + 4)*(n + 24)\n | ibivibiv/math_instruct | |
Simplify (a**(2/9)*a/(a/(a**0/a)))/(a**7)**(-42) assuming a is positive.\n | a**(2639/9)\n | ibivibiv/math_instruct | |
Simplify ((m**(-11)*m**(-6)/m*m**(5/6)/(m*m**(-3)))**(-2/75))**(2/25) assuming m is positive.\n | m**(182/5625)\n | ibivibiv/math_instruct | |
Put -3, 0.0146, 0, 80, 0.2 in decreasing order.\n | 80, 0.2, 0.0146, 0, -3\n | ibivibiv/math_instruct | |
Let o = 0.21 + -4.71. Let d = -5 - o. Put -5, d, -0.2 in ascending order.\n | -5, d, -0.2\n | ibivibiv/math_instruct | |
Suppose 2*i - 3*i = -15. Suppose i*g - 12*g = 0. Solve -h + 10 = t + t, 5*h + 3*t - 22 = g for h.\n | 2\n | ibivibiv/math_instruct | |
Which is smaller: 0 or -7929?\n | -7929\n | ibivibiv/math_instruct | |
Let y(b) = b**4 - b**2 + b + 1. Let p(m) = 6*m**5 - 6*m**4 + 14*m**2 - 6*m - 6. Let l(c) = p(c) + 6*y(c). What is the third derivative of l(g) wrt g?\n | 360*g**2\n | ibivibiv/math_instruct | |
Suppose 0 = 9*o - 37265 - 16438. Does 39 divide o?\n | True\n | ibivibiv/math_instruct | |
Does 10 divide 100705?\n | False\n | ibivibiv/math_instruct | |
Suppose 0 = 2*d + 8 + 48. Let x = -25 - d. Solve x*t - 2*t - 15 = 4*g, -3*g - t = 13 for g.\n | -4\n | ibivibiv/math_instruct | |
Find the third derivative of 15*x**4 + 31*x**3 - x**2 - 31*x**3 wrt x.\n | 360*x\n | ibivibiv/math_instruct | |
What is the fourth biggest value in 0.16, 9, 23, -0.4?\n | -0.4\n | ibivibiv/math_instruct | |
Find the first derivative of -2*x**2*y**2 - 6*x**2*y + 26811*x**2 + 7793171*y**2 wrt x.\n | -4*x*y**2 - 12*x*y + 53622*x\n | ibivibiv/math_instruct | |
In base 7, what is 3211 - -3?\n | 3214\n | ibivibiv/math_instruct | |
Let h = -23/233 - 19063/2796. Let o = 16471/654 - 2/109. Find the common denominator of o and h.\n | 12\n | ibivibiv/math_instruct | |
Let u = 14.38617 - 714.80717. Let h = -1352 + 651. Let o = h - u. What is o rounded to one dp?\n | -0.6\n | ibivibiv/math_instruct | |
What is the second smallest value in 5, 4, 0, -4/3?\n | 0\n | ibivibiv/math_instruct | |
Simplify (c/c**1*c/(c**5/c))/(c**6/(c**(3/2)*c))*(c**(-1/2)/c)**15/(c*c**0)**(-23) assuming c is positive.\n | c**(-6)\n | ibivibiv/math_instruct | |
Collect the terms in 7*y**2 + 857219818214*y - 857219818214*y.\n | 7*y**2\n | ibivibiv/math_instruct | |
Let i = 17 - 6. Let o = -6 + i. Let q(k) = k**2 - 5*k + 4. Is q(o) a multiple of 2?\n | True\n | ibivibiv/math_instruct | |
Let h = -6 - -6. Suppose 3*m + 2*n - 26 = h, 2 = -4*n - 18. What is the units digit of m?\n | 2\n | ibivibiv/math_instruct | |
What is -2 divided by 55?\n | -2/55\n | ibivibiv/math_instruct | |
Does 41 divide 1190?\n | False\n | ibivibiv/math_instruct | |
Solve -27 = 3*s + 4*m, 0 = 2*s - 5*m + 2*m + 1 for s.\n | -5\n | ibivibiv/math_instruct | |
Let w = -60 - -117. Let h be (-572)/12 + 2/(-6). Let n = w + h. Which is the biggest value? (a) 4 (b) -1/2 (c) -3 (d) n\n | d\n | ibivibiv/math_instruct | |
Let m = 10 + -10.39. Let c = 90 - 90.05. Let n = m - c. What is n rounded to one decimal place?\n | -0.3\n | ibivibiv/math_instruct | |
What is the hundreds digit of 7717?\n | 7\n | ibivibiv/math_instruct | |
Simplify ((h**(-3/2)/h**1)/((h*h/(h**(3/2)/h))/h**(1/4)))/(h/(h*h**13)*(h**(1/9)/h)/h)**15 assuming h is positive.\n | h**(2635/12)\n | ibivibiv/math_instruct | |
What is -10 - (-17 + (-10 + 13 - -9))?\n | -5\n | ibivibiv/math_instruct | |
Suppose -2*x + 2*a + 2 = -6, 3*x - 2 = 5*a. Let r = 10 - x. Is r less than 1?\n | False\n | ibivibiv/math_instruct | |
637628 divided by 318814\n | 2\n | ibivibiv/math_instruct | |
Suppose -u + s + 6 = 0, 3*u - 2*s = 5*u. Let i be u/6*4*(-20)/(-8). Suppose -i*t - 2*x + 99 = 0, -5*x + x + 46 = 2*t. Does 2 divide t?\n | False\n | ibivibiv/math_instruct | |
Put together -162096921 and 1.5.\n | -162096919.5\n | ibivibiv/math_instruct | |
Let a(k) = -2*k**2 + 8*k + 2. Let z = 283 - 282. Let y(d) = d. Give z*a(q) - 10*y(q).\n | -2*q**2 - 2*q + 2\n | ibivibiv/math_instruct | |
Simplify (l**(-2))**(1/32)*l/((l/(l/(l**8/l)))/l)*l*(l*l**(10/7)*l)/l assuming l is positive.\n | l**(-183/112)\n | ibivibiv/math_instruct | |
Is -858 greater than -858?\n | False\n | ibivibiv/math_instruct | |
Is (-2388)/(-18) + 2/6 prime?\n | False\n | ibivibiv/math_instruct | |
Let c(i) = i. Let v be (-4)/12*9/3. Let u(r) = -r + r - 5*r. Let z(p) = v*u(p) - 6*c(p). Let a(y) = -3*y**2. Calculate a(z(q)).\n | -3*q**2\n | ibivibiv/math_instruct | |
Is 13418115923 prime?\n | True\n | ibivibiv/math_instruct | |
Four letters picked without replacement from htbthtt. What is prob of picking 1 h and 3 t?\n | 8/35\n | ibivibiv/math_instruct | |
What is the value of 1 + 2 + (3 - (-2 + 5))?\n | 3\n | ibivibiv/math_instruct |
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