#### Simpson Rule

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

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

method 2:
"Simpson Rule"

"""

def method_2(boundary: list[int], steps: int) -> float:
# "Simpson Rule"
# int(f) = delta_x/2 * (b-a)/3*(f1 + 4f2 + 2f_3 + ... + fn)
"""
Calculate the definite integral of a function using Simpson's Rule.
:param boundary: A list containing the lower and upper bounds of integration.
:param steps: The number of steps or resolution for the integration.
:return: The approximate integral value.

>>> round(method_2([0, 2, 4], 10), 10)
2.6666666667
>>> round(method_2([2, 0], 10), 10)
-0.2666666667
>>> round(method_2([-2, -1], 10), 10)
2.172
>>> round(method_2([0, 1], 10), 10)
0.3333333333
>>> round(method_2([0, 2], 10), 10)
2.6666666667
>>> round(method_2([0, 2], 100), 10)
2.5621226667
>>> round(method_2([0, 1], 1000), 10)
0.3320026653
>>> round(method_2([0, 2], 0), 10)
Traceback (most recent call last):
...
ZeroDivisionError: Number of steps must be greater than zero
>>> round(method_2([0, 2], -10), 10)
Traceback (most recent call last):
...
ZeroDivisionError: Number of steps must be greater than zero
"""
if steps <= 0:
raise ZeroDivisionError("Number of steps must be greater than zero")

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  # number of steps or resolution
boundary = [a, b]  # boundary of integration
y = method_2(boundary, steps)
print(f"y = {y}")

if __name__ == "__main__":
import doctest

doctest.testmod()
main()
```