from __future__ import annotations

import sys







def     A__	(       __A						):







    '''simple docstring'''
    if n < 0:
        raise ValueError("""Negative arguments are not supported"""						)
    return _fib(__A						)[0]







def     A__	(       __A						):







    '''simple docstring'''
    if n == 0:  # (F(0), F(1))
        return (0, 1)

    # F(2n) = F(n)[2F(n+1) − F(n)]
    # F(2n+1) = F(n+1)^2+F(n)^2
    _lowerCamelCase    ,				_lowerCamelCase  :		List[Any]			    =    _fib(n // 2						)
    _lowerCamelCase  :		List[Any]			    =    a * (b * 2 - a)
    _lowerCamelCase  :		Optional[int]			    =    a * a + b * b
    return (d, c + d) if n % 2 else (c, d)


if __name__ == "__main__":
    lowerCAmelCase      :				Union[str, Any]     			=int(sys.argv[1])
    print(F"""fibonacci({n}) is {fibonacci(n)}""")





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()




