Hi,
I know this is an older thread, but thought it may help others. Here is a sample using Mechanize - you do need the Crypt::SSLeay module installed for it to work.
use strict;
use WWW::Mechanize;
use HTTP::Cookies;
my $url = "http://www.facebook.com";
my $appurl = "http://apps.facebook.com/inthemafia";
my $username = 'your@email';
my $password = 'yourpass';
my $mech = WWW::Mechanize->new();
$mech->cookie_jar(HTTP::Cookies->new());
$mech->get($url);
$mech->form_name('menubar_login');
$mech->field(email => $username);
$mech->field(pass => $password);
$mech->click();
my $facebook_content = $mech->content();
# go to an app url
$mech->get($appurl);
my $app_content = $mech->content();
print "$app_content\n";
