






SCREAMING_SNAKE_CASE								=  1000

def        _lowerCamelCase		(  __A      :							float	) ->   float:
    return x * x

def        _lowerCamelCase		(  __A      :							str						,						__A      :							float						,						__A      :							float						,						__A      :							int = 4	) ->   float:
    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

    _UpperCAmelCase			: Dict     					=			(b - a) / N_STEPS
    _UpperCAmelCase			: Optional[int]     					=			function(__A	) + function(__A	)

    for i in range(1						,						__A	):
        _UpperCAmelCase			: Union[str, Any]     					=			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()












def        _lowerCamelCase		(  __A      :							dict						,						__A      :							int	) ->   str:
    if not root or root not in binary_tree_mirror_dictionary:
        return
    _UpperCAmelCase					,	_UpperCAmelCase			: int     					=			binary_tree_mirror_dictionary[root][:2]
    _UpperCAmelCase			: int     					=			[right_child, left_child]
    binary_tree_mirror_dict(__A						,						__A	)
    binary_tree_mirror_dict(__A						,						__A	)

def        _lowerCamelCase		(  __A      :							dict						,						__A      :							int = 1	) ->   dict:
    if not binary_tree:
        raise ValueError('''binary tree cannot be empty'''	)
    if root not in binary_tree:
        _UpperCAmelCase			: Dict     					=			f'''root {root} is not present in the binary_tree'''
        raise ValueError(__A	)
    _UpperCAmelCase			: int     					=			dict(__A	)
    binary_tree_mirror_dict(__A						,						__A	)
    return binary_tree_mirror_dictionary


if __name__ == "__main__":
  SCREAMING_SNAKE_CASE								=  {1: [2, 3], 2: [4, 5], 3: [6, 7], 7: [8, 9]}
  print(F'Binary tree: {binary_tree}')
  SCREAMING_SNAKE_CASE								=  binary_tree_mirror(binary_tree, 5)
  print(F'Binary tree mirror: {binary_tree_mirror_dictionary}')




