Issues implementing Simpsons Rule correctly using python

Question

I have a code for Simpsons rule for definite integrals that I created myself. For some reason, this code is not outputting the correct value. My current function is y = x^3, the value of N is 4, the value of a is 0 and the value of b is 2. According to Simpsons rule, the area must then be 1/6(0^ 3(4 * (0.5 ^ 3))(2 * (1.0 ^ 3))(4 * (1.5 ^ 3))(2 3)). Calculating that by hand, the value is correctly 4. However, in my program, using the same logic, the output becomes 8 and changes based on the value of n. In my mind, the area should not change greatly just because n is changed to another positive number. It should in fact, become more precise. You can see what I mean from my code.

def trapezoid(lb, rb, r):
   width = (rb-lb)/r
   currentX = lb
   area = currentX ** 3
   yes = "4"
   currentX += width
   while currentX < rb:
       if yes == "4":
            area += (4 * (currentX ** 3))
            yes = "2"
            currentX += width 
            continue
        if yes == "2":
            area += (2 * (currentX ** 3))
            yes = "4"
            currentX += width 
            continue
   area +=  ((rb) ** 3)
   area *= ((rb - lb)/(3 * rb))
   return area
lftBount = int(input("Enter the left bound:"))
rgtBount = int(input("Enter the right bound:"))
Repeat = int(input("How many times do you want"))
print(trapezoid(lftBount,rgtBount,Repeat))

I've run this through in my head and on paper several times, could someone point me in the direction where I went wrong?

Answer 1

From https://www.intmath.com/integration/6-simpsons-rule.php it seems to me that there is only one small mistake in your code when you divide (last statement in your function) your area by the right bound:

area *= ((rb - lb)/(3 * rb))

whereas it should be divided by the number of segments, so:

area *= (rb - lb) / (3 * r)

With this modification the output produced for input values 0, 2, and 4 is indeed 4.0.

Here is a modification of your code, where I made function f(x) = x ** 3 a parameter of trapezoid so that it can be easily changed by another function. I also simplified a bit the body of the while loop.

def trapezoid(lb, rb, r, f):  #  f = function used
    width = (rb - lb) / r
    currentX = lb
    area = f(currentX)
    multby4 = True
    currentX += width
    while currentX < rb:
        if multby4:
            area += 4 * f(currentX)
        else:
            area += 2 * f(currentX)
        currentX += width
        multby4 = not multby4  #  switch bit multby4 for the next iteration
    area += f(rb)
    area *= (rb - lb) / (3 * r)
    return area

def f(x):
    return x ** 3
lftBount = int(input("Enter the left bound:"))
rgtBount = int(input("Enter the right bound:"))
Repeat = int(input("How many times do you want"))
print(trapezoid(lftBount, rgtBount, Repeat, f))