Simpsons 3 by 8

 #Numerical integration by Simpson's 3/8 rule

from math import *

def f(x):

    return 1/(1+x)

a,b,n =eval(input('Input lower limit (a), upper limit (b) & no. of steps(multiple of 3)(n): '))

h = (b - a)/float(n)

x = [a+h*i for i in range(n+1)]

y=[f(x[i]) for i in range(n+1)] 

intgrl=y[0] + y[-1]

for i in range(1,n):

    if i%3==0:

        intgrl+=2*y[i]

    else:

        intgrl+=3*y[i]

intgrl=(3*h/8)*intgrl     

print('Integral using Simpson\'s 3/8 rule = ',intgrl)         

Output Screen:

Input lower limit (a), upper limit (b) & no. of steps(multiple of 3)(n): 0,1,3

Integral using Simpson's 3/8 rule =  0.6937500000000001

Another Code

#Numerical integration by Simpsons 3/8 rule

from math import *

def f(x):

    return sin(x)

a=0

b=pi/2

n=int(input ("enter number of intervals,n  "))

h=(b-a)/n

integral=f(a)+f(b)

for i in range(1,n):

    x=a+i*h

    if (i%3==0):

        integral=integral+2*f(x)

    else:

        integral=integral+3*f(x)

integral=(3*h/8)*integral        

print (integral)