from scipy import random
from scipy.integrate import quad
import numpy as np


a = 0
b = np.pi
N = 10000000
xrand = random.uniform(a,b,N)


def f(x):
    return np.sin(x)

integral = 0.0

for i in range(N):
    integral += f(xrand[i])

answer = (b-a)/float(N)*integral

print("The integral from 0 to pi of sin(x): ", answer)
print(quad(f,0,np.pi)[0])