


import sys



def      __lowerCAmelCase    (				snake_case						:     int    ,   snake_case						:     list[int]			)							->				int:
   if not numbers:
      return 0
   if target == 0 and target in numbers:
      return 0
   if not isinstance(snake_case    ,   (list, tuple)			) or not all(
       isinstance(snake_case    ,   snake_case			) for number in numbers			):
      raise ValueError("""numbers must be an iterable of integers"""			)

   __lowerCamelCase:					Union[str, Any]	 =						0
   __lowerCamelCase:					str	 =						sys.maxsize

   while right < len(snake_case			):
      curr_sum += numbers[right]
      while curr_sum >= target and left <= right:
         __lowerCamelCase:					str	 =						min(snake_case    ,   right - left + 1			)
         curr_sum -= numbers[left]
         left += 1
      right += 1

   return 0 if min_len == sys.maxsize else min_len






_A		:					Union[str, Any]          =							1_000



def      __lowerCAmelCase    (				snake_case						:     float			)							->				float:
   return x * x



def      __lowerCAmelCase    (				snake_case						:     Optional[int]    ,   snake_case						:     float    ,   snake_case						:     float    ,   snake_case						:     int = 4			)							->				float:
   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

   __lowerCamelCase:					List[str]	 =						(b - a) / N_STEPS
   __lowerCamelCase:					Optional[Any]	 =						function(snake_case			) + function(snake_case			)

   for i in range(1    ,   snake_case			):
      __lowerCamelCase:					Dict	 =						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()


