old_contents: # Python Packages
  import random
  
  # External Packages
  import numpy as np
  
  
  def sin_theta_sum(theta):
      return np.sin(theta)
  
  
  def gen_random_value(count, rmin, rmax):
      value = 0
      for i in range(count):
          value += np.random.uniform(rmin, rmax)
          # test_range(rmin, rmax, value)
      return value
  
  
  def run_monte_carlo(samples, function, func_coeff, func_vars):
      value = 0
      for i in range(samples):
          if i % 10000 == 0:
              print(i)
          value += function(func_vars)
      value = value*func_coeff/samples
      return value
  
  
  def sin_monte_element(rmax):
      value = gen_random_value(8, 0, rmax)
      result = sin_theta_sum(value)
      return result
  
  
  def main():
      rmax = np.pi/8
      samples = 10000000
      coefficient = 1000000
      volume = np.power(np.pi/8, 8)
      func_coeff = coefficient*volume
      func_vars = rmax
      result = run_monte_carlo(samples, sin_monte_element, func_coeff, func_vars)
      print(result)
  
  
  def test_range(rmin, rmax, value):
      if (value <= rmin or value >= rmax):
          print(False)
  
  
  main()
  
new_contents: # Python Packages
  import random
  
  # External Packages
  import numpy as np
  
  
  def sin_theta_sum(variables):
      theta = 0
      for var in variables:
          theta += var
      return np.sin(theta)
  
  
  def gen_random_variables(count, rmin, rmax):
      variables = []
      for i in range(count):
          variables.append(np.random.uniform(rmin, rmax))
          # test_range(rmin, rmax, value)
      return variables
  
  
  def run_monte_carlo(samples, function, func_coeff, func_vars):
      value = 0
      for i in range(samples):
          if i % 10000 == 0:
              print(i)
          value += function(func_vars)
      value = value*func_coeff/samples
      return value
  
  
  def sin_monte_element(rmax):
      value = gen_random_variables(8, 0, rmax)
      result = sin_theta_sum(value)
      return result
  
  
  def main():
      rmax = np.pi/8
      samples = 10000000
      coefficient = 1000000
      volume = np.power(rmax, 8)
      func_coeff = coefficient*volume
      func_vars = rmax
      result = run_monte_carlo(samples, sin_monte_element, func_coeff, func_vars)
      print(result)
  
  
  def test_range(rmin, rmax, value):
      if (value <= rmin or value >= rmax):
          print(False)
  
  
  main()
  
subject: Adjust code to restore generality.