I prefer to use the submit_form() method. Also, you need to check for errors, either manually or by setting autocheck.

#!/usr/bin/perl
use strict;
use WWW::Mechanize;
my $browser = WWW::Mechanize->new( autocheck=>1 );
$browser->get('http://www.google.com');
$browser->submit_form(
    form_name => 'f',
    fields => {
        q => 'langley public library',
    },
);
print $browser->content();
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