


"""simple docstring"""
from __future__ import annotations






def 						lowercase				(	_snake_case		: list[int | float]	,  _snake_case		: int	,  _snake_case		: int	)	->int | float:
	"""simple docstring"""





	if len(_snake_case	) == 0:
		raise ValueError('''find_min() arg is an empty sequence'''	)
	if (
	    left >= len(_snake_case	)
	    or left < -len(_snake_case	)
	    or right >= len(_snake_case	)
	    or right < -len(_snake_case	)
	):
		raise IndexError('''list index out of range'''	)
	if left == right:
		return nums[left]
	__snake_case      :		List[Any]         =							(left + right) >> 1  # the middle
	__snake_case      :		Dict         =							find_min(_snake_case	,  _snake_case	,  _snake_case	)  # find min in range[left, mid]
	__snake_case      :		Tuple         =							find_min(_snake_case	,  mid + 1	,  _snake_case	)  # find min in range[mid + 1, right]

	return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
			import doctest

			doctest.testmod(verbose=True)









"""simple docstring"""
SCREAMING_SNAKE_CASE					:       List[Any]							   =							1000






def 						lowercase				(	_snake_case		: float	)	->float:
	"""simple docstring"""





	return x * x






def 						lowercase				(	_snake_case		: Union[str, Any]	,  _snake_case		: float	,  _snake_case		: float	,  _snake_case		: int = 4	)	->float:
	"""simple docstring"""





	assert callable(
	    _snake_case	), f"""the function(object) passed should be callable your input : {function}"""
	assert isinstance(_snake_case	,  (float, int)	), f"""a should be float or integer your input : {a}"""
	assert isinstance(function(_snake_case	)	,  (float, int)	), (
	    "the function should return integer or float return type of your function, "
	    f"""{type(_snake_case	)}"""
	)
	assert isinstance(_snake_case	,  (float, int)	), f"""b should be float or integer your input : {b}"""
	assert (
	    isinstance(_snake_case	,  _snake_case	) 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

	__snake_case      :		Tuple         =							(b - a) / N_STEPS
	__snake_case      :		Union[str, Any]         =							function(_snake_case	) + function(_snake_case	)

	for i in range(1	,  _snake_case	):
		__snake_case      :		List[str]         =							a + h * i
		result += function(_snake_case	) * (4 if i % 2 else 2)

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


if __name__ == "__main__":
			import doctest

			doctest.testmod()





