Adding doctests in simpson_rule.py (#10269)

* Adding doctests in simpson_rule.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Update maths/simpson_rule.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update maths/simpson_rule.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Adding doctests in simpson_rule.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Adding doctests in simpson_rule.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Adding doctests in simpson_rule.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Adding doctests in simpson_rule.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Adding doctests in simpson_rule.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update simpson_rule.py

* Adding doctests in simpson_rule.py

* Adding doctests in simpson_rule.py

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

maths/simpson_rule.py

@@ -1,7 +1,7 @@
 """
 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'
+This method is the classical approach of summing 'Equally Spaced Abscissas'
 
 method 2:
 "Simpson Rule"
@@ -9,9 +9,41 @@ method 2:
 """
 
 
-def method_2(boundary, steps):
+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]
@@ -41,11 +73,14 @@ def f(x):  # enter your function here
 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
+    steps = 10.0  # number of steps or resolution
-    boundary = [a, b]  # define boundary of integration
+    boundary = [a, b]  # boundary of integration
     y = method_2(boundary, steps)
     print(f"y = {y}")
 
 
 if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
     main()