Some of you keep using the phrase "completely trained". Palpatine wasn't even completely trained. yes he did say that Plaugeus taught him everything he knew, but he still didn't know how to do it all, just that it could be acomplished.
As far as I know there is no canon confirmation of, nor any hard evidence to support, the theory that Palpatine was an apprentice of Darth Plaugeus. All we have is a guess made by Darth Wong, based on the fact that Palpatine smiled when he mentioned that Plaugeus was killed by his apprentice, and that the murder of Plaugeus could have roughly coincided with the time of Anakin's immaculate conception.
There is some strong evidence against this theory, when you consider that Palpatine later mentioned that the ability to create or preserve life that Plaugeus had posessed had been lost for a long time, and that while Palpatine was describing Plaugeus to Anakin in the theatre his tone of voice seemed to indicate that Plaugeus had not been around in many eons. I recall reading a similiar theory after Episode I came out speculating that Palpatine himself was Anakin's father, which seems equally unlikely. With all due respect to Darth Wong, who might still be right, he has been wrong in the past, and taking one of his theories as canon is, frankly, absurd (and based on what I've seen him write here, I'm sure he would agree with me).
In summary, I think it's foolhardy to assume that Palpatine was the apprentice of Darth Plageus when we have no official confirmation of the fact, just a theory.
"Here's a nickel, kid. Get yourself a better computer."