You can try this:

my $ua = LWP::UserAgent->new();
my $res = $ua->request(POST "http://www.example.com"
  Content_Type => 'form-data',
  Content      =>
    [ "var1" => "foo",
      "var2" => "bar",
      "var3[id]" => "foobar"
    ]);
[download]

But it seems you have broken web-application, which cannot parse requests well. Do you use CGI.pm for it?