You might want to try to use WWW::Mechanize instead.. it can make this type of thing extremely easy:

use WWW::Mechanize;
use strict;
use warnings;
my $mech = WWW::Mechanize->new;

my $sequence = '...';

$mech->get('http://www.arabidopsis.org/Blast/');
$mech->submit_form(
  form_name => 'myForm',
  fields => {
    'Algorithm' => 'blastx',
    'BlastTargetSet' => 'ATH1_pep',
    'QueryText' => $sequence,
  },
);

print $mech->content;
[download]

Note: your code had 'Algorithem' but the actual field element is 'Algorithm'