'''simple docstring'''


def    _lowerCamelCase       ( lowerCamelCase_   :				int = 30  ):



     """simple docstring"""





     UpperCAmelCase_				:  Optional[int]  = exponent + 2
     UpperCAmelCase_				:  Union[str, Any]  = (1 + 5**0.5) / 2
     UpperCAmelCase_				:  Optional[Any]  = (phi**fibonacci_index - (phi - 1) ** fibonacci_index) / 5**0.5

     return int(lowerCamelCase_  )


if __name__ == "__main__":
 print(f'''{solution() = }''')







lowerCAmelCase      :				Union[str, Any]     			=1000







def     A__	(       __A						):







    '''simple docstring'''
    return x * x







def     A__	(       __A ,			__A ,			__A ,			__A = 4						):







    '''simple docstring'''
    assert callable(
        __A						), F"""the function(object) passed should be callable your input : {function}"""
    assert isinstance(__A ,			(float, int)						), F"""a should be float or integer your input : {a}"""
    assert isinstance(function(__A						) ,			(float, int)						), (
        "the function should return integer or float return type of your function, "
        F"""{type(__A						)}"""
    )
    assert isinstance(__A ,			(float, int)						), F"""b should be float or integer your input : {b}"""
    assert (
        isinstance(__A ,			__A						) and precision > 0
    ), F"""precision should be positive integer your input : {precision}"""

    # just applying the formula of simpson for approximate integration written in
    # mentioned article in first comment of this file and above this function

    _lowerCamelCase  :		Optional[Any]			    =    (b - a) / N_STEPS
    _lowerCamelCase  :		str			    =    function(__A						) + function(__A						)

    for i in range(1 ,			__A						):
        _lowerCamelCase  :		str			    =    a + h * i
        result += function(__A						) * (4 if i % 2 else 2)

    result *= h / 3
    return round(__A ,			__A						)


if __name__ == "__main__":
    import doctest

    doctest.testmod()




