can a law enforcementagency post an ad say in Eros , then when you respond to the Hotel bust you .?? or is that intrapment.???

What you describe is a regular sting operation and is legal.  Entrapment means that the police actually made you commit a crime you otherwise wouldn't have committed as opposed to just creating an opportunity.

This is done quite often in a large SE city. LE even puts up fake reviews.

It is easier for some doughnut munchers than solving real crime and I can tell you that the easy way rules in bureaucracy, especially in law enforcement.