## Python, math, simpson_rule.py

``````"""
Numerical integration or quadrature for a smooth function f with known values at x_i

This method is the classical approach of suming 'Equally Spaced Abscissas'

method 2:
"Simpson Rule"

"""

def method_2(boundary, steps):
# "Simpson Rule"
# int(f) = delta_x/2 * (b-a)/3*(f1 + 4f2 + 2f_3 + ... + fn)
h = (boundary[1] - boundary[0]) / steps
a = boundary[0]
b = boundary[1]
x_i = make_points(a, b, h)
y = 0.0
y += (h / 3.0) * f(a)
cnt = 2
for i in x_i:
y += (h / 3) * (4 - 2 * (cnt % 2)) * f(i)
cnt += 1
y += (h / 3.0) * f(b)
return y

def make_points(a, b, h):
x = a + h
while x < (b - h):
yield x
x = x + h

def f(x):  # enter your function here
y = (x - 0) * (x - 0)
return y

def main():
a = 0.0  # Lower bound of integration
b = 1.0  # Upper bound of integration
steps = 10.0  # define number of steps or resolution
boundary = [a, b]  # define boundary of integration
y = method_2(boundary, steps)
print(f"y = {y}")

if __name__ == "__main__":
main()
``````