





from __future__ import annotations





def  a_       (							_lowercase ,		_lowercase ,		_lowercase ,		):







						if not all((nth_term, start_term_a, common_ratio_r)     ):
												return []
						_UpperCamelCase    :      int						     =					[]
						_UpperCamelCase    :      Optional[int]						     =					1
						_UpperCamelCase    :      str						     =					common_ratio_r
						for _ in range(int(_lowercase     )     ):
												if not series:
																		series.append(_lowercase     )
												else:
																		power += 1
																		series.append(float(start_term_a * multiple     )     )
																		_UpperCamelCase    :      Dict						     =					pow(float(_lowercase     ) ,		_lowercase     )
						return series


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						UpperCamelCase_     =float(input("""Enter the last number (n term) of the Geometric Series"""))
						UpperCamelCase_     =float(input("""Enter the starting term (a) of the Geometric Series"""))
						UpperCamelCase_     =float(
						    input("""Enter the common ratio between two terms (r) of the Geometric Series""")
						)
						print("""Formula of Geometric Series => a + ar + ar^2 ... +ar^n""")
						print(geometric_series(nth_term, start_term_a, common_ratio_r))










"""simple docstring"""




UpperCamelCase_     =1_000





def  a_       (							_lowercase     ):
						return x * x





def  a_       (							_lowercase ,		_lowercase ,		_lowercase ,		_lowercase = 4     ):
						assert callable(
						    _lowercase     ), F"""the function(object) passed should be callable your input : {function}"""
						assert isinstance(_lowercase ,		(float, int)     ), F"""a should be float or integer your input : {a}"""
						assert isinstance(function(_lowercase     ) ,		(float, int)     ), (
						    "the function should return integer or float return type of your function, "
						    F"""{type(_lowercase     )}"""
						)
						assert isinstance(_lowercase ,		(float, int)     ), F"""b should be float or integer your input : {b}"""
						assert (
						    isinstance(_lowercase ,		_lowercase     ) and precision > 0
						), F"""precision should be positive integer your input : {precision}"""

						# just applying the formula of simpson for approximate integration written in
						# mentioned article in first comment of this file and above this function

						_UpperCamelCase    :      str						     =					(b - a) / N_STEPS
						_UpperCamelCase    :      Dict						     =					function(_lowercase     ) + function(_lowercase     )

						for i in range(1 ,		_lowercase     ):
												_UpperCamelCase    :      List[Any]						     =					a + h * i
												result += function(_lowercase     ) * (4 if i % 2 else 2)

						result *= h / 3
						return round(_lowercase ,		_lowercase     )


if __name__ == "__main__":
						import doctest

						doctest.testmod()



