code: 
  
  
  
  
  
  '''simple docstring'''
  
  
  import math as m
  
  
  
  
  def    __a (     UpperCAmelCase       ,			UpperCAmelCase       ,			UpperCAmelCase=0.001    )      ->Optional[int]:
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  
  
  	return (f(a + h    ) - f(a - h    )) / (2 * h)
  
  
  
  
  def    __a (     UpperCAmelCase       ,			UpperCAmelCase=0       ,			UpperCAmelCase=100       ,			UpperCAmelCase=0.0_001       ,			UpperCAmelCase=1E-6       ,			UpperCAmelCase=False    )      ->Optional[Any]:
  
  
  
  	"""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
  
  				_lowerCamelCase				:	Tuple				    =       lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
  				_lowerCamelCase    ,  _lowerCamelCase    ,  _lowerCamelCase				:	int				    =       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}}}")
  
  
style_context: 
  
  
  
  
  
  '''simple docstring'''
  
  
  from __future__ import annotations
  
  
  
  class 							__UpperCAmelCase  :
  
  
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		def __init__(self						:      Any      ,      _lowerCAmelCase						:      int      ):
  			A							  =      value
  			A							  =      None
  			A							  =      None
  
  
  
  
  
  
  class 							__UpperCAmelCase  :
  
  
  
  
  
  
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		__lowerCAmelCase 				=    42
  
  
  
  
  
  
  
  		def __init__(self						:      List[str]      ):
  			A							  =      0
  
  
  
  
  
  
  
  		def        A     (self						:      Dict      ,      _lowerCAmelCase						:      Node | None      ,      _lowerCAmelCase						:      int      ):
  			if node is None:
  				return
  
  			if path_sum == self.target:
  				self.paths += 1
  
  			if node.left:
  				self.depth_first_search(node.left      ,      path_sum + node.left.value      )
  			if node.right:
  				self.depth_first_search(node.right      ,      path_sum + node.right.value      )
  
  
  
  
  
  
  
  		def        A     (self						:      Optional[Any]      ,      _lowerCAmelCase						:      Node | None      ,      _lowerCAmelCase						:      int | None = None      ):
  			if node is None:
  				return 0
  			if target is not None:
  				A							  =      target
  
  			self.depth_first_search(_lowerCAmelCase      ,      node.value      )
  			self.path_sum(node.left      )
  			self.path_sum(node.right      )
  
  			return self.paths
  
  
  if __name__ == "__main__":
  				import doctest
  
  				doctest.testmod()
  
  