
def 			A_			(					lowercase						, lowercase = 1000      )     ->							str:


     """simple docstring"""







     if (not isinstance(lowercase						, lowercase      )) or (digit_position <= 0):
          raise ValueError("""Digit position must be a positive integer"""      )
     elif (not isinstance(lowercase						, lowercase      )) or (precision < 0):
          raise ValueError("""Precision must be a nonnegative integer"""      )

     # compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
     # accurate
     UpperCAmelCase_						:    Union[str, Any]    					=  (
         4 * _subsum(lowercase						, 1						, lowercase      )
         - 2 * _subsum(lowercase						, 4						, lowercase      )
         - _subsum(lowercase						, 5						, lowercase      )
         - _subsum(lowercase						, 6						, lowercase      )
     )

     # return the first hex digit of the fractional part of the result
     return hex(int((sum_result % 1) * 16      )      )[2:]




def 			A_			(					lowercase						, lowercase						, lowercase      )     ->							float:


     """simple docstring"""







     UpperCAmelCase_						:    List[str]    					=  0.0
     for sum_index in range(digit_pos_to_extract + precision      ):
          UpperCAmelCase_						:    Optional[Any]    					=  8 * sum_index + denominator_addend
          if sum_index < digit_pos_to_extract:
               # if the exponential term is an integer and we mod it by the denominator
               # before dividing, only the integer part of the sum will change;
               # the fractional part will not
               UpperCAmelCase_						:    Optional[Any]    					=  pow(
                   16						, digit_pos_to_extract - 1 - sum_index						, lowercase      )
          else:
               UpperCAmelCase_						:    Dict    					=  pow(16						, digit_pos_to_extract - 1 - sum_index      )
          total += exponential_term / denominator
     return total


if __name__ == "__main__":
       import doctest

       doctest.testmod()



"""simple docstring"""







def 			A_			(					lowercase = 99_8001      )     ->							int:


     """simple docstring"""







     for number in range(n - 1						, 9999						, -1      ):
          UpperCAmelCase_						:    Union[str, Any]    					=  str(lowercase      )

          # checks whether 'str_number' is a palindrome.
          if str_number == str_number[::-1]:
               UpperCAmelCase_						:    List[str]    					=  999

               # if 'number' is a product of two 3-digit numbers
               # then number is the answer otherwise fetch next number.
               while divisor != 99:
                    if (number % divisor == 0) and (len(str(number // divisor      )      ) == 3.0):
                         return number
                    divisor -= 1
     raise ValueError("""That number is larger than our acceptable range."""      )


if __name__ == "__main__":
       print(f"""{solution() = }""")

