The documentation example is of a GET request. I have found POST documentation to be lacking, and here's a function to easily simulate submitting form data:

<?php
# $host includes host and path and filename
    # ex: "myserver.com/this/is/path/to/file.php"
# $query is the POST query data
    # ex: "a=thisstring&number=46&string=thatstring
# $others is any extra headers you want to send
    # ex: "Accept-Encoding: compress, gzip\r\n"
function post($host,$query,$others=''){
    $path=explode('/',$host);
    $host=$path[0];
    unset($path[0]);
    $path='/'.(implode('/',$path));
    $post="POST $path HTTP/1.1\r\nHost: $host\r\nContent-type: application/x-www-form-urlencoded\r\n${others}User-Agent: Mozilla 4.0\r\nContent-length: ".strlen($query)."\r\nConnection: close\r\n\r\n$query";
    $h=fsockopen($host,80);
    fwrite($h,$post);
    for($a=0,$r='';!$a;){
        $b=fread($h,8192);
        $r.=$b;
        $a=(($b=='')?1:0);
    }
    fclose($h);
    return $r;
}
?>