I am familiar with BeautifulSoup and urllib2 to scrape data from a webpage. However, what if a parameter needs to be entered into the page before the result that I want to
In addition with the answers already given, you could simply do a request on that page. Using your browser you could always inspect the Network (under Tools/Web Developer tools) behaviors and actions when you interact with the page. E.g. http://www.freemaptools.com/ajax/getaandb.php?a=Florida_Usa&b=New%20York_Usa&c=6052 -> request query for getting the results page you are expecting. Request that page and scrape the field you wanted to. IMHO, page requests are way faster than screen scraping (case-to-case basis).
But of course, you could always do screen scraping/browser simulation also (Mechanize, Splinter) and use headless browsers (PhantomJS, etc.) or the browser driver of the browser you want to use.