

'''simple docstring'''

def  UpperCamelCase(	UpperCAmelCase_      ):

 for insert_index, insert_value in enumerate(collection[1:]      ):
  UpperCAmelCase			:      int		   =					insert_index
  while insert_index >= 0 and insert_value < collection[insert_index]:
   UpperCAmelCase			:      Union[str, Any]		   =					collection[insert_index]
   insert_index -= 1
  if insert_index != temp_index:
   UpperCAmelCase			:      Optional[Any]		   =					insert_value
 return collection


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

 testmod()

 lowercase__            =     input("Enter numbers separated by a comma:\n").strip()
 lowercase__            =     [int(item) for item in user_input.split(",")]
 print(f'''{insertion_sort(unsorted) = }''')







'''simple docstring'''

from __future__ import annotations

from collections.abc import Callable




def  UpperCamelCase(	UpperCAmelCase_    ,			UpperCAmelCase_    ,			UpperCAmelCase_    ,			UpperCAmelCase_ = 1_00    ,			):
 UpperCAmelCase			:      Any		   =					x_start
 UpperCAmelCase			:      int		   =					fnc(UpperCAmelCase_      )
 UpperCAmelCase			:      str		   =					0.0

 for _ in range(UpperCAmelCase_      ):
  # Approximates small segments of curve as linear and solve
  # for trapezoidal area
  UpperCAmelCase			:      List[Any]		   =					(x_end - x_start) / steps + xa
  UpperCAmelCase			:      int		   =					fnc(UpperCAmelCase_      )
  area += abs(fxa + fxa      ) * (xa - xa) / 2

  # Increment step
  UpperCAmelCase			:      List[str]		   =					xa
  UpperCAmelCase			:      List[Any]		   =					fxa
 return area


if __name__ == "__main__":




 def  UpperCamelCase(	UpperCAmelCase_      ):
  return x**3

 print("f(x) = x^3")
 print("The area between the curve, x = -10, x = 10 and the x axis is:")
 lowercase__            =     10
 while i <= 100000:
  lowercase__            =     trapezoidal_area(f, -5, 5, i)
  print(f'''with {i} steps: {area}''')
  i *= 10




