Like there's "shared website host", I hope there's a database host.
It's like getting an IP, user name and password and just connecting to that database.
I think that would be better instead of trying to setup such a server - rent dedicated server, configure software (prone to many errors).
So I'm looking for this company that take this seriously and have a cluster (for reliability) of MySQL servers from which I can rent some allocation.
Oh, and I'm looking for this service in Europe.