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# Numerical integration to calculate value of pi

from numpy import *
from scipy import integrate

r = 1.0                          # radius of the circle
def f(x):
return sqrt(r**2 - x**2)         # equation of circle

res = integrate.quad(f, 0, 1)    # integrate from 0 to r

print res[0] * 4, pi             #compare area x 4 to area of unit circle