run.sh

Enter function to be integrated for f(x): x**2
Enter lower limit / bound of integration: 1
<class 'str'>
<class 'int'>
You entered: 1
Enter upper limit / bound of integration: 3
You entered: 3
Enter number of segments of integration: 20
You entered: 20
Result: 8.66666666666667

simpsonsRule.py

def simpsonsRule(f, a, b, n):
    """
       simpsonsRule: (int) -> float
       Parameters:
           n: integer representing the number of segments being used to
              approximate the integral
       Pre conditions:
           Function bounds() declared that returns lower and upper bounds of integral.
           Function f(x) declared that returns the evaluated equation at point x.
           Parameters passed.
       Post conditions:
           Returns float equal to the approximate integral of f(x) from a to b
           using Simpson's rule.
       Description:
           Returns the approximation of an integral. Works as of python 3.3.2
           REQUIRES NO MODULES to be imported, especially not non standard ones.
           -Code by TechnicalFox
    """
    sum = float()
    sum += f(a) #evaluating first point
    sum += f(b) #evaluating last point
    width=(b-a)/(2*n) #width of segments
    oddSum = float()
    evenSum = float()
    for i in range(1,n): #evaluating all odd values of n (not first and last)
       oddSum += f(2*width*i+a)
    sum += oddSum * 2
    for i in range(1,n+1): #evaluating all even values of n (not first and last)
       evenSum += f(width*(-1+2*i)+a)
    sum += evenSum * 4
    return sum * width/3


def main():
    # read in f
    value = input("Enter function to be integrated for f(x): ")
    value = "def f(x):\n\treturn " + value

    capture = {}
    exec (value, globals(), capture)
    f = capture['f']

    a = input("Enter lower limit / bound of integration: ")
    print (type(a))
    a = int(a)
    print (type(a))
    print ("You entered:", a)

    while True:
       b = input("Enter upper limit / bound of integration: ")
       b = int(b)
       print ("You entered:", b)
       if b > a:
           break
       print ("Upper bound must be greater than lower bound...")

    n = input("Enter number of segments of integration: ")
    n = int(n)
    print ("You entered:", n)
    print ("Result:", simpsonsRule(f, a, b, n))


if __name__ == "__main__":
    main()