The Repair & Optimise feature merely issues the MySQL commands REPAIR TABLE and OPTIMIZE TABLE, see https://dev.mysql.com/doc/refman/5.1/en/repair-table.html and https://dev.mysql.com/doc/refman/5.1/en/optimize-table.html As you can read in the official MySQL documentation, written and maintained by Oracle, these are security neutral commands. In fact you should not even need to run them if your host didn't have a severely overloaded and misconfigured database server. MySQL tables don't crash on their own volition, they crash because the server is so stressed that threads are crashing in the middle of a write operation.
In the end of the day try issuing these commands from phpMyAdmin. Select the tables you want and from the "With selected" dropdown at the bottom of the page first select "Repair" and then "Optimize".
I still do not understand how issuing two very standard, security neutral MySQL commands which are also used by phpMyAdmin (that they already have installed on their server!) makes Admin Tools a malicious piece of software. They have no idea what they are talking about. I strongly recommend no longer using Interspace because they've pretty much proved to you that they don't understand how their own servers work!!!
Nicholas K. Dionysopoulos
Lead Developer and Director
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