This shows a program to calculate Integration using Trapezoidal Rule with a desired Accuracy

Trapezoid.py

import numpy as np
original_value = np.pi/4
def f(x):
    return 1/(1+x*x)#1st step is done

def trapizoid(f,a,b,tol):
    fa = f(a); fb = f(b);I = 0
    n =10; it = 1#Iteration number
    while True:
        h = (b-a)/n
        sum = 0
        for i in range(1,n):#It takes i = 1 upto i = n-1
            sum = sum + f(a+i*h)
        sum = h/2*(fa+2*sum+fb)
        if abs(sum-I)<=tol:
            break
        it += 1#same as it = it + 1
        I = sum
        n += 15
    return sum

tol = 1.0e-6
Integration_value = trapizoid(f,0,1,tol)
print("The value of Integration : ",Integration_value)
print("Error : ", abs(Integration_value-original_value))
#OutPut:
#The value of Integration :  0.7853956979142137
#Error :  2.46548323457052e-06