def radiationExposure(start, stop, step):

     '''

     Computes and returns the amount of radiation exposed

     to between the start and stop times. Calls the

     function f (defined for you in the grading script)

     to obtain the value of the function at any point.

     start: integer, the time at which exposure begins

     stop: integer, the time at which exposure ends

     step: float, the width of each rectangle. You can assume that

       the step size will always partition the space evenly.

     returns: float, the amount of radiation exposed to

       between start and stop times.

     '''

     # FILL IN YOUR CODE HERE...

     area = 0

     while start <  stop:

         area = area + f(start) * step

         start += step

     return area

 # 6.00 Problem Set 3

 #

 # Hangman game

 #

 # -----------------------------------

 # Helper code

 # You don't need to understand this helper code,

 # but you will have to know how to use the functions

 # (so be sure to read the docstrings!)

 import random

 import string

 WORDLIST_FILENAME = "words.txt"

 def loadWords():

     """

     Returns a list of valid words. Words are strings of lowercase letters.

     Depending on the size of the word list, this function may

     take a while to finish.

     """

     print "Loading word list from file..."

     # inFile: file

     inFile = open(WORDLIST_FILENAME, 'r', 0)

     # line: string

     line = inFile.readline()

     # wordlist: list of strings

     wordlist = string.split(line)

     print "  ", len(wordlist), "words loaded."

     return wordlist

 def chooseWord(wordlist):

     """

     wordlist (list): list of words (strings)

     Returns a word from wordlist at random

     """

     return random.choice(wordlist)

 # end of helper code

 # -----------------------------------

 # Load the list of words into the variable wordlist

 # so that it can be accessed from anywhere in the program

 wordlist = loadWords()

 def isWordGuessed(secretWord, lettersGuessed):

     '''

     secretWord: string, the word the user is guessing

     lettersGuessed: list, what letters have been guessed so far

     returns: boolean, True if all the letters of secretWord are in

         lettersGuessed; False otherwise

     '''

     # FILL IN YOUR CODE HERE...

     for c in secretWord:

         if c not in lettersGuessed:

             return False

     return True

 def getGuessedWord(secretWord, lettersGuessed):

     '''

     secretWord: string, the word the user is guessing

     lettersGuessed: list, what letters have been guessed so far

     returns: string, comprised of letters and underscores that represents

       what letters in secretWord have been guessed so far.

     '''

     # FILL IN YOUR CODE HERE...

     guess = ""

     for c in secretWord:

         if c in lettersGuessed:

             guess += c

         else:

             guess += "_ "

     return guess

 def getAvailableLetters(lettersGuessed):

     '''

     lettersGuessed: list, what letters have been guessed so far

     returns: string, comprised of letters that represents what letters have not

       yet been guessed.

     '''

     # FILL IN YOUR CODE HERE...

     available = ""

     for c in string.ascii_lowercase:

         if c not in lettersGuessed:

             available += c

     return available

 def hangman(secretWord):

     '''

     secretWord: string, the secret word to guess.

     Starts up an interactive game of Hangman.

     * At the start of the game, let the user know how many

       letters the secretWord contains.

     * Ask the user to supply one guess (i.e. letter) per round.

     * The user should receive feedback immediately after each guess

       about whether their guess appears in the computers word.

     * After each round, you should also display to the user the

       partially guessed word so far, as well as letters that the

       user has not yet guessed.

     Follows the other limitations detailed in the problem write-up.

     '''

     # FILL IN YOUR CODE HERE...

     print "Welcome to the game Hangman!"

     print "I am thinking of a word that is", len(secretWord), "letters long."

     print "-------------"

     lettersGuessed = []

     mistakesMade = 0

     availableLetters = string.ascii_lowercase

     while mistakesMade < 8 and not isWordGuessed(secretWord, lettersGuessed):

         print "You have", 8 - mistakesMade, "guesses left."

         print "Available letters:", availableLetters

         guess = raw_input("Please guess a letter: ").lower()

         if guess in lettersGuessed:

             print("Oops! You've already guessed that letter: " +

                 getGuessedWord(secretWord, lettersGuessed))

         elif guess in secretWord:

             lettersGuessed.append(guess)

             print "Good guess:", getGuessedWord(secretWord, lettersGuessed)

         else:

             mistakesMade += 1

             lettersGuessed.append(guess)

             print("Oops! That letter is not in my word: " +

                 getGuessedWord(secretWord, lettersGuessed))

         availableLetters = getAvailableLetters(lettersGuessed)

         print "------------"

     if isWordGuessed(secretWord, lettersGuessed):

         print "Congratulations, you won!"

     else:

         print("Sorry, you ran out of guesses. The word was " + secretWord +

             ".")

 # When you've completed your hangman function, uncomment these two lines

 # and run this file to test! (hint: you might want to pick your own

 # secretWord while you're testing)

 secretWord = chooseWord(wordlist).lower()

 hangman(secretWord)