






from collections.abc import Callable

def      _lowerCamelCase	(						__A    :							Tuple		,		__A    :							Optional[int]		,		__A    :							Optional[Any] )      ->					float:
    _UpperCAmelCase				:      List[Any]			  =				a
    _UpperCAmelCase				:      Optional[int]			  =				b
    if function(_A ) == 0:  # one of the a or b is a root for the function
        return a
    elif function(_A ) == 0:
        return b
    elif (
        function(_A ) * function(_A ) > 0
    ):  # if none of these are root and they are both positive or negative,
        # then this algorithm can't find the root
        raise ValueError('''could not find root in given interval.''' )
    else:
        _UpperCAmelCase				:      Tuple			  =				start + (end - start) / 2.0
        while abs(start - mid ) > 10**-7:  # until precisely equals to 10^-7
            if function(_A ) == 0:
                return mid
            elif function(_A ) * function(_A ) < 0:
                _UpperCAmelCase				:      Union[str, Any]			  =				mid
            else:
                _UpperCAmelCase				:      str			  =				mid
            _UpperCAmelCase				:      Dict			  =				start + (end - start) / 2.0
        return mid

def      _lowerCamelCase	(						__A    :							Union[str, Any] )      ->					float:
    return x**3 - 2 * x - 5


if __name__ == "__main__":
       print(bisection(f, 1, 1000))

       import doctest

       doctest.testmod()












from math import pow, sqrt

def      _lowerCamelCase	(						*__A    :							float )      ->					bool:
    _UpperCAmelCase				:      str			  =				len(__A ) > 0 and all(value > 0.0 for value in values )
    return result

def      _lowerCamelCase	(						__A    :							float		,		__A    :							float )      ->					float | ValueError:
    return (
        round(sqrt(molar_mass_a / molar_mass_a )		,		6 )
        if validate(__A		,		__A )
        else ValueError('''Input Error: Molar mass values must greater than 0.''' )
    )

def      _lowerCamelCase	(						__A    :							float		,		__A    :							float		,		__A    :							float )      ->					float | ValueError:
    return (
        round(effusion_rate * sqrt(molar_mass_a / molar_mass_a )		,		6 )
        if validate(__A		,		__A		,		__A )
        else ValueError(
            '''Input Error: Molar mass and effusion rate values must greater than 0.''' )
    )

def      _lowerCamelCase	(						__A    :							float		,		__A    :							float		,		__A    :							float )      ->					float | ValueError:
    return (
        round(effusion_rate / sqrt(molar_mass_a / molar_mass_a )		,		6 )
        if validate(__A		,		__A		,		__A )
        else ValueError(
            '''Input Error: Molar mass and effusion rate values must greater than 0.''' )
    )

def      _lowerCamelCase	(						__A    :							float		,		__A    :							float		,		__A    :							float )      ->					float | ValueError:
    return (
        round(molar_mass / pow(effusion_rate_a / effusion_rate_a		,		2 )		,		6 )
        if validate(__A		,		__A		,		__A )
        else ValueError(
            '''Input Error: Molar mass and effusion rate values must greater than 0.''' )
    )


def      _lowerCamelCase	(						__A    :							float		,		__A    :							float		,		__A    :							float )      ->					float | ValueError:
    return (
        round(pow(effusion_rate_a / effusion_rate_a		,		2 ) / molar_mass		,		6 )
        if validate(__A		,		__A		,		__A )
        else ValueError(
            '''Input Error: Molar mass and effusion rate values must greater than 0.''' )
    )




