simpson.py

import math

def f(x): # change this to the function of your choice
    squared = math.pow(x, 2)
    return math.sqrt(squared+1)

a = 0 # start
b = 2 # end
n = 6 # increase for more accuracy
dx = (b-a)/n
print(f"dx = {dx}")
result = 0

xis = range(n+1)
for i in xis:
    xi = a + (dx*i)
    t = f(xi)
    if i == 0 or i == n:
        result += t
        print(f"{i}: {t}")
    elif i%2==1:
        result += 4 * t
        print(f"{i}: {t*4}")
    else:
        result += 2 * t
        print(f"{i}: {t*2}")

print(f"result: {result}")
print(f"dx/3: {dx/3}")
result *= (dx/3)

print(f"result * (dx/3): {result}")

trapeziod.py

import math

def f(x):
    squared = math.pow(x, 2)
    return math.sqrt(squared + 1)

a = 0
b = 2
n = 26
dx = (b-a)/n
xis = range(n+1)
print(f"dx = {dx}")

result = 0

for i in xis:
    xi = a+(dx*i)
    if i == 0 or i == n:
        t = f(xi)
        print(f"{i}: {t}")
        result += t
    else:
        t = f(xi)
        print(f"{i}: {t*2}")
        result += t

print(f"result: {result}")
print(f"dx/2: {dx/2}")
result *= (dx/2)

print(f"result * (dx/2): {result}")