function example() {
    $exampleUser = $_POST['username'];
    $examplePass = $_POST['password'];
    $example = new example_model();
    $exampleResults= $example->do_example($exampleUser, $examplePass);
    require_once("example1.php");
}

function do_example($exampleUser, $examplePass) {
    $exampleResults = mysqli_fetch_assoc($connection->query("SELECT * FROM users WHERE username = '$exampleUser' AND password = '$examplePass'");
return $exampleResults;
}

<?php
    echo $example['username'];
    // RESULTS IN DISPLAYING "ExampleName"
?>

<?php
        echo $example['username'];
        // ERROR BECAUSE IT DOESN'T HAVE THE DATA STORED ANYMORE
        // AND I DON'T WANT TO CALL A FUNCTION TO GET THE DATA FOR THE USER AGAIN AFTER EACH PAGE CHANGE
?>