"""⏎
Author : Syed Faizan ( 3rd Year IIIT Pune )⏎
Github : faizan2700⏎
⏎
Purpose : You have one function f(x) which takes float integer and returns⏎
float you have to integrate the function in limits a to b.⏎
The approximation proposed by Thomas Simpsons in 1743 is one way to calculate integration.⏎
⏎
( read article : https://cp-algorithms.com/num_methods/simpson-integration.html )⏎
⏎
simpson_integration() takes function,lower_limit=a,upper_limit=b,precision and⏎
returns the integration of function in given limit.⏎
"""⏎
⏎
# constants⏎
# the more the number of steps the more accurate⏎
N_STEPS = 1000⏎
⏎
⏎
def f(x: float) -> float:⏎
    return x * x⏎
⏎
⏎
"""⏎
Summary of Simpson Approximation :⏎
⏎
By simpsons integration :⏎
1.integration of fxdx with limit a to b is = f(x0) + 4 * f(x1) + 2 * f(x2) + 4 * f(x3) + 2 * f(x4)..... + f(xn)⏎
where x0 = a⏎
xi = a + i * h⏎
xn = b⏎
"""⏎
⏎
⏎
def simpson_integration(function, a: float, b: float, precision: int = 4) -> float:⏎
⏎
    """⏎
    Args:⏎
        function : the function which's integration is desired⏎
        a : the lower limit of integration⏎
        b : upper limit of integraion⏎
        precision : precision of the result,error required default is 4⏎
⏎
    Returns:⏎
        result : the value of the approximated integration of function in range a to b⏎
⏎
    Raises:⏎
        AssertionError: function is not callable⏎
        AssertionError: a is not float or integer⏎
        AssertionError: function should return float or integer⏎
        AssertionError: b is not float or integer⏎
        AssertionError: precision is not positive integer⏎
⏎
    >>> simpson_integration(lambda x : x*x,1,2,3)⏎
    2.333⏎
⏎
    >>> simpson_integration(lambda x : x*x,'wrong_input',2,3)⏎
    Traceback (most recent call last):⏎
        ...⏎
    AssertionError: a should be float or integer your input : wrong_input⏎
⏎
    >>> simpson_integration(lambda x : x*x,1,'wrong_input',3)⏎
    Traceback (most recent call last):⏎
        ...⏎
    AssertionError: b should be float or integer your input : wrong_input⏎
⏎
    >>> simpson_integration(lambda x : x*x,1,2,'wrong_input')⏎
    Traceback (most recent call last):⏎
        ...⏎
    AssertionError: precision should be positive integer your input : wrong_input⏎
    >>> simpson_integration('wrong_input',2,3,4)⏎
    Traceback (most recent call last):⏎
        ...⏎
    AssertionError: the function(object) passed should be callable your input : wrong_input⏎
⏎
    >>> simpson_integration(lambda x : x*x,3.45,3.2,1)⏎
    -2.8⏎
⏎
    >>> simpson_integration(lambda x : x*x,3.45,3.2,0)⏎
    Traceback (most recent call last):⏎
        ...⏎
    AssertionError: precision should be positive integer your input : 0⏎
⏎
    >>> simpson_integration(lambda x : x*x,3.45,3.2,-1)⏎
    Traceback (most recent call last):⏎
        ...⏎
    AssertionError: precision should be positive integer your input : -1⏎
⏎
    """⏎
    assert callable(⏎
        function⏎
    ), f"the function(object) passed should be callable your input : {function}"⏎
    assert isinstance(a, float) or isinstance(⏎
        a, int⏎
    ), f"a should be float or integer your input : {a}"⏎
    assert isinstance(function(a), float) or isinstance(⏎
        function(a), int⏎
    ), f"the function should return integer or float return type of your function, {type(a)}"⏎
    assert isinstance(b, float) or isinstance(⏎
        b, int⏎
    ), f"b should be float or integer your input : {b}"⏎
    assert (⏎
        isinstance(precision, int) and precision > 0⏎
    ), f"precision should be positive integer your input : {precision}"⏎
⏎
    # just applying the formula of simpson for approximate integraion written in⏎
    # mentioned article in first comment of this file and above this function⏎
⏎
    h = (b - a) / N_STEPS⏎
    result = function(a) + function(b)⏎
⏎
    for i in range(1, N_STEPS):⏎
        a1 = a + h * i⏎
        result += function(a1) * (4 if i % 2 else 2)⏎
⏎
    result *= h / 3⏎
    return round(result, precision)⏎
⏎
⏎
if __name__ == "__main__":⏎
    import doctest⏎
⏎
    doctest.testmod()⏎