Passing updated value to function (twitter api max_id problems) - php

Question

I am trying to work with the Twitter search API, I found a php library that does authentication with app-only auth and I added the max_id argument to it, however, I would like to run 450 queries per 15 minutes (as per the rate-limit) and I am not sure about how to pass the max_id. So I run it first with the default 0 value, and then it gets the max_id result from the API's response and runs the function again, but this time with the retrieved max_id value and does this 450 times. I tried a few things, and I can get the max_id result after calling the function, but I don't know how to pass it back and tell it to call the function with the updated value.
<?php
function search_for_a_term($bearer_token, $query, $result_type='mixed', $count='15', $max_id='0'){
$url = "https://api.twitter.com/1.1/search/tweets.json"; // base url
$q = $query; // query term
$formed_url ='?q='.$q; // fully formed url
if($result_type!='mixed'){$formed_url = $formed_url.'&result_type='.$result_type;} // result type - mixed(default), recent, popular
if($count!='15'){$formed_url = $formed_url.'&count='.$count;} // results per page - defaulted to 15
$formed_url = $formed_url.'&include_entities=true'; // makes sure the entities are included
if($max_id!='0'){$formed_url=$formed_url.'&max_id='.$max_id;}
$headers = array(
"GET /1.1/search/tweets.json".$formed_url." HTTP/1.1",
"Host: api.twitter.com",
"User-Agent: jonhurlock Twitter Application-only OAuth App v.1",
"Authorization: Bearer ".$bearer_token."",
);
$ch = curl_init(); // setup a curl
curl_setopt($ch, CURLOPT_URL,$url.$formed_url); // set url to send to
curl_setopt($ch, CURLOPT_HTTPHEADER, $headers); // set custom headers
ob_start(); // start ouput buffering
$output = curl_exec ($ch); // execute the curl
$retrievedhtml = ob_get_contents(); // grab the retreived html
ob_end_clean(); //End buffering and clean output
curl_close($ch); // close the curl
$result= json_decode($retrievedhtml, true);
return $result;
}
$results=search_for_a_term("mybearertoken", "mysearchterm");
/* would like to get all kinds of info from here and put it into a mysql database */
$max_id=$results["search_metadata"]["max_id_str"];
print $max_id; //this gives me the max_id for that page
?>
I know that there are must be some existing libraries that do this, but I can't use any of the libraries, since none of them have updated to the app-only auth yet.
EDIT: I put a loop in the beginning of the script, to run e.g. 3 times, and then put a print statement to see what happens, but it only prints out the same max_id, doesn't access three different ones.
do{
$result = search_for_a_term("mybearertoken", "searchterm", $max_id);
$max_id = $result["search_metadata"]["max_id_str"];
$i++;
print ' '.$max_id.' ';
}while($i < 3);