Try again after a reboot, maybe?
When you open your trash, it doesn't show something like "restore items"? If it was on your desktop, most likely it was just a shortcut to the program, not the program itself. You can get it back by right click on the program in All Programs/Send To/Desktop.
may i know which operating system you are using?
You can try these things.
1. open trash(Mac)/Recycle bin(win) than select the indesign icon, try Right-Clicking on the file within the Trash and select ‘Put Back’ from the contextual menu(Mac) on windows after selecting the indesign icon in Recycle bin > right click restore.
2. Go to application folder on Mac , open indesign folder, select the indesign application icon create an alias. or on windows all programs. Indesign > rightclick indesign icon> send to desktop(create shortcut).