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"""

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()