"""
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 1:
"extended trapezoidal rule"

"""


def method_1(boundary, steps):
 # "extended trapezoidal rule"
 # int(f) = dx/2 * (f1 + 2f2 + ... + 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 / 2.0) * f(a)
 for i in x_i:
 # print(i)
 y += h * f(i)
 y += (h / 2.0) * 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_1(boundary, steps)
 print(f"y = {y}")


if __name__ == "__main__":
 main()