As opposed to query reformulation oriented towards changes made by a user to specify the information need more precisely, a post-search query modeling is a technique of exploiting syntax variation of gradually extended query which depending on some other factors like e.g. the resource, database or the key word alignment, facilitates the searching process. The study into modeling query submitted to some search engines that utilize different translation semantic paradigms is motivated by a real-world's challenges to retrieve heterogeneous textual documents from the web. For a couple of language pairs, we develop a user-centered framework for imposing the Hidden Web traffic optimization. In literature Hidden Web is the World Wide Web facet usually missed by standard information systems. Our data set contains variety of query types submitted to translingual systems that perform a number of syntax-driven indexing being evaluated by constructing a precision trend function, the one that intensifies the relevance set of the system responses from a perspective of dramatic reduction of those outside the user's interest.