How to set new AUTO_INCREMENT value?
Parameter replacement only works for WHERE clauses, it won't work for the kind of query you're trying to run.

You need to insert $start_value directly into the query string. If that value comes from an un-trustworthy source then obviously you need to sanitise it and make sure it falls within the correct bounds yourself:

$start_value = (int)$start_value; // Make sure it's an integer

// Do any other checks you need to here (bounds checking, etc.)

// Build the query string and run it
$sql = "ALTER TABLE {tripletex_invoice} AUTO_INCREMENT = $start_value";
db_query($sql);