Prueba así:
Código PHP:
<?php
require_once("HttpConnection.php");
$http = new HttpConnection();
$http->setCookiePath("/cookies/");
$http->init();
$apost = array('usuario' =>"usuario", 'password' => "pass");
echo ($http->post("https://dominio/entrada.asp", $apost));
echo ($http->get("https://dominio/documento.asp?var=var"));
$http->close();
El close() te borra las cookies