
'''simple docstring'''






from __future__ import annotations

from fractions import Fraction







def 		A_       (	_lowerCAmelCase   :    int				,	_lowerCAmelCase   :    int							):



      """simple docstring"""




      return (
          num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
      )







def 		A_       (	_lowerCAmelCase   :    int							):



      """simple docstring"""




      _lowerCamelCase				:   Dict								=   []
      _lowerCamelCase				:   Optional[Any]								=   11
      _lowerCamelCase				:   str								=   int("1" + "0" * digit_len							)
      for num in range(_lowerCAmelCase				,	_lowerCAmelCase							):
            while den <= 99:
                  if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
                        if is_digit_cancelling(_lowerCAmelCase				,	_lowerCAmelCase							):
                              solutions.append(F'{num}/{den}'							)
                  den += 1
            num += 1
            _lowerCamelCase				:   Any								=   10
      return solutions







def 		A_       (	_lowerCAmelCase   :    int = 2							):



      """simple docstring"""




      _lowerCamelCase				:   int								=   1.0
      for fraction in fraction_list(_lowerCAmelCase							):
            _lowerCamelCase				:   List[Any]								=   Fraction(_lowerCAmelCase							)
            result *= frac.denominator / frac.numerator
      return int(_lowerCAmelCase							)


if __name__ == "__main__":
 print(solution())

'''simple docstring'''






def 		A_       (	_lowerCAmelCase   :    float							):



      """simple docstring"""




      return 10 - x * x







def 		A_       (	_lowerCAmelCase   :    float				,	_lowerCAmelCase   :    float							):



      """simple docstring"""




      if equation(_lowerCAmelCase							) * equation(_lowerCAmelCase							) >= 0:
            raise ValueError("Wrong space!"							)

      _lowerCamelCase				:   List[str]								=   a
      while (b - a) >= 0.0_1:
            # Find middle point
            _lowerCamelCase				:   Union[str, Any]								=   (a + b) / 2
            # Check if middle point is root
            if equation(_lowerCAmelCase							) == 0.0:
                  break
            # Decide the side to repeat the steps
            if equation(_lowerCAmelCase							) * equation(_lowerCAmelCase							) < 0:
                  _lowerCamelCase				:   Union[str, Any]								=   c
            else:
                  _lowerCamelCase				:   Any								=   c
      return c


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 print(bisection(-2, 5))
 print(bisection(0, 6))