UPDATE:
here is some sample code (one CGI script and one command-line script) to demonstrate how WWW::Mechanize will "fill-in" the hidden values for you:

(foo.cgi)

#!/usr/bin/perl -T

use strict;
use warnings;

use CGI qw(:standard);
use Data::Dumper;

print header,start_html;
if (param('go')) {
   print ul(li[map {"$_ = ". param($_)} param()]);
}
else {
   print start_form,
      textfield('foo'),
      hidden(-name=>'hidden1',-value=>'one'),
      hidden(-name=>'hidden2',-value=>'two'),
      hidden(-name=>'hidden3',-value=>'three'),
      submit('go'),
      end_form,
   ;
}

----------------------------------------------------
(foo.pl)

#!/usr/bin/perl

use strict;
use warnings;
use WWW::Mechanize;

my $agent = WWW::Mechanize->new();
$agent->get('http://localhost/path/to/foo.cgi');

$agent->form(1);
$agent->field('foo','bar');
$agent->click('go');

print $agent->{content};
[download]

jeffa

L-LL-L--L-LL-L--L-LL-L--
-R--R-RR-R--R-RR-R--R-RR
B--B--B--B--B--B--B--B--
H---H---H---H---H---H---
(the triplet paradiddle with high-hat)