





'''simple docstring'''


from __future__ import annotations

from collections.abc import Callable




def  __a			(  UpperCAmelCase							,      UpperCAmelCase							,      UpperCAmelCase							,      UpperCAmelCase = 100							,      )   ->Optional[Any]:



	"""simple docstring"""







	A					=   x_start
	A					=   fnc(_lowerCamelCase     )
	A					=   0.0

	for _ in range(_lowerCamelCase     ):
		# Approximates small segments of curve as linear and solve
		# for trapezoidal area
		A					=   (x_end - x_start) / steps + xa
		A					=   fnc(_lowerCamelCase     )
		area += abs(fxa + fxa     ) * (xa - xa) / 2

		# Increment step
		A					=   xa
		A					=   fxa
	return area


if __name__ == "__main__":




				def  __a			(  UpperCAmelCase     )   ->Union[str, Any]:



					"""simple docstring"""







					return x**3

				print('f(x) = x^3')
				print('The area between the curve, x = -10, x = 10 and the x axis is:')
				_lowerCamelCase					:						Optional[int]					     =							10
				while i <= 10_0000:
								_lowerCamelCase					:						Optional[int]					     =							trapezoidal_area(f, -5, 5, i)
								print(f"with {i} steps: {area}")
								i *= 10


from .number_theory.prime_numbers import next_prime



class     snake_case_			:






   def __init__( self							:	Tuple      ,		lowercase_							:	int      ,		lowercase_							:	int | None = None      ,		lowercase_							:	float | None = None      ,		)   ->		None:
       lowercase__					:  Optional[Any]          =							size_table
       lowercase__					:  Tuple          =							[None] * self.size_table
       lowercase__					:  List[str]          =							0.75 if lim_charge is None else lim_charge
       lowercase__					:  Optional[Any]          =							1 if charge_factor is None else charge_factor
       lowercase__					:  list          =							[]
       lowercase__					:  dict          =							{}






   def  __UpperCamelCase	( self							:	List[Any]    )   ->		Optional[Any]:
       return self._keys






   def  __UpperCamelCase	( self							:	Any    )   ->		List[Any]:
       return sum(1 for slot in self.values if slot is not None    ) / (
           self.size_table * self.charge_factor
       )






   def  __UpperCamelCase	( self							:	int      ,		lowercase_							:	Union[str, Any]    )   ->		Dict:
       return key % self.size_table






   def  __UpperCamelCase	( self							:	Union[str, Any]      ,		lowercase_							:	Any    )   ->		List[str]:
       print(F'''step {step_ord}'''    )
       print(list(range(len(self.values    )    )    )    )
       print(self.values    )






   def  __UpperCamelCase	( self							:	Tuple      ,		lowercase_							:	List[Any]    )   ->		Union[str, Any]:
       lowercase__					:  Any          =							1
       lowercase__					:  Dict          =							values
       for value in values:
           self.insert_data(lowercase_    )
           self._step_by_step(lowercase_    )
           i += 1






   def  __UpperCamelCase	( self							:	Tuple      ,		lowercase_							:	Dict      ,		lowercase_							:	Optional[Any]    )   ->		Any:
       lowercase__					:  str          =							data
       lowercase__					:  List[str]          =							data






   def  __UpperCamelCase	( self							:	int      ,		lowercase_							:	Any      ,		lowercase_							:	int=None    )   ->		int:
       lowercase__					:  Dict          =							self.hash_function(key + 1    )

       while self.values[new_key] is not None and self.values[new_key] != key:
           if self.values.count(lowercase_    ) > 0:
               lowercase__					:  List[Any]          =							self.hash_function(new_key + 1    )
           else:
               lowercase__					:  List[str]          =							None
               break

       return new_key






   def  __UpperCamelCase	( self							:	Union[str, Any]    )   ->		Optional[int]:
       lowercase__					:  Tuple          =							[value for value in self.values if value is not None]
       lowercase__					:  Any          =							next_prime(self.size_table      ,		factor=2    )
       self._keys.clear()
       lowercase__					:  Tuple          =							[None] * self.size_table  # hell's pointers D: don't DRY ;/
       for value in survivor_values:
           self.insert_data(lowercase_    )







   def  __UpperCamelCase	( self							:	Dict      ,		lowercase_							:	Optional[int]    )   ->		int:
       lowercase__					:  List[str]          =							self.hash_function(lowercase_    )

       if self.values[key] is None:
           self._set_value(lowercase_      ,		lowercase_    )

       elif self.values[key] == data:
           pass

       else:
           lowercase__					:  List[Any]          =							self._collision_resolution(lowercase_      ,		lowercase_    )
           if collision_resolution is not None:
               self._set_value(lowercase_      ,		lowercase_    )
           else:
               self.rehashing()
               self.insert_data(lowercase_    )



