

import math as m

def 			__snake_case	(   __UpperCamelCase  :   List[str]							,__UpperCamelCase  :   int							,__UpperCamelCase  :   Union[str, Any]=0.001						):



      """simple docstring"""

      return (f(a + h						) - f(a - h						)) / (2 * h)

def 			__snake_case	(   __UpperCamelCase  :   List[Any]							,__UpperCamelCase  :   List[str]=0							,__UpperCamelCase  :   int=100							,__UpperCamelCase  :   Union[str, Any]=0.0001							,__UpperCamelCase  :   Dict=1E-6							,__UpperCamelCase  :   int=False						):



      """simple docstring"""

      A_	     =							xa  # set the initial guess
      A_	     =							[a]
      A_	     =							abs(f(__UpperCamelCase						)						)
      A_	     =							lambda __UpperCamelCase						: calc_derivative(__UpperCamelCase							,__UpperCamelCase							,h=__UpperCamelCase						)  # noqa: E731  Derivative of f(x)
      for _ in range(__UpperCamelCase						):
            if fa(__UpperCamelCase						) == 0:
                  raise ValueError("No converging solution found"						)
            A_	     =							a - f(__UpperCamelCase						) / fa(__UpperCamelCase						)  # Calculate the next estimate
            if logsteps:
                  steps.append(__UpperCamelCase						)
            if error < maxerror:
                  break
      else:
            raise ValueError("Iteration limit reached, no converging solution found"						)
      if logsteps:
            # If logstep is true, then log intermediate steps
            return a, error, steps
      return a, error


if __name__ == "__main__":
      from matplotlib import pyplot as plt

      __a						:List[str]            = lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
      __a      ,			__a      ,			__a						:List[str]            = newton_raphson(
          f, xa=10, maxiter=1000, step=1e-6, logsteps=True
      )
      plt.plot([abs(f(x)) for x in steps])
      plt.xlabel('step')
      plt.ylabel('error')
      plt.show()
      print(F"solution = {{{solution:f}}}, error = {{{error:f}}}")


__a						:Dict            = {hex(i)[2:]: i for i in range(16)}  # Use [:2] to strip off the leading '0x'

def 			__snake_case	(   __UpperCamelCase  :   str						):



      """simple docstring"""

      A_	     =							hex_string.strip().lower()
      if not hex_string:
            raise ValueError("Empty string was passed to the function"						)
      A_	     =							hex_string[0] == "-"
      if is_negative:
            A_	     =							hex_string[1:]
      if not all(char in hex_table for char in hex_string						):
            raise ValueError("Non-hexadecimal value was passed to the function"						)
      A_	     =							0
      for char in hex_string:
            A_	     =							16 * decimal_number + hex_table[char]
      return -decimal_number if is_negative else decimal_number


if __name__ == "__main__":
      from doctest import testmod

      testmod()