






def   snake_case		(				UpperCAmelCase						:							Any,    UpperCAmelCase						:							int = 10_00 ):
				if (not isinstance(lowerCAmelCase__,    lowerCAmelCase__ )) or (digit_position <= 0):
								raise ValueError('Digit position must be a positive integer' )
				elif (not isinstance(lowerCAmelCase__,    lowerCAmelCase__ )) 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
				A									=   (
				    4 * _subsum(lowerCAmelCase__,    1,    lowerCAmelCase__ )
				    - 2 * _subsum(lowerCAmelCase__,    4,    lowerCAmelCase__ )
				    - _subsum(lowerCAmelCase__,    5,    lowerCAmelCase__ )
				    - _subsum(lowerCAmelCase__,    6,    lowerCAmelCase__ )
				)

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







def   snake_case		(				UpperCAmelCase						:							str,    UpperCAmelCase						:							int,    UpperCAmelCase						:							Union[str, Any] ):
				A									=   0.0
				for sum_index in range(digit_pos_to_extract + precision ):
								A									=   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
												A									=   pow(
												    16,    digit_pos_to_extract - 1 - sum_index,    lowerCAmelCase__ )
								else:
												A									=   pow(16,    digit_pos_to_extract - 1 - sum_index )
								total += exponential_term / denominator
				return total


if __name__ == "__main__":
					import doctest

					doctest.testmod()







def 			UpperCamelCase       (				lowerCAmelCase__ = 30						):
					'''simple docstring'''
					lowercase		      =		exponent + 2
					lowercase		      =		(1 + 5**0.5) / 2
					lowercase		      =		(phi**fibonacci_index - (phi - 1) ** fibonacci_index) / 5**0.5

					return int(lowerCAmelCase__						)


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




