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What is my answer ? First let me quote from R.A. Torrey .... I think that my will must conform to His, that I must trust in His promises, that I must believe that He is good and means good for me, then my prayers will prepare me for whatever comes my way.

Your short answer: God changes your mind, but never ever changes His own. Right?

Now I realize the determinist model precludes one from understanding that God changes His mind (although Scripture clearly says He does). But what does that position leave for petitionary prayer? Apart from the meeting of some ceremonial requirement (i.e. one doing something meaningless because one feels one is instructed to perform such a meaningless act), what purpose is served in asking for anything (particularly for others) in sincere prayer to God?

Isn't it true that the determinist model leaves no real expectation of an answer to petitionary prayer for others? Again, then, apart from the meeting of a ceremonial requirement (defined above), why would any good determinist pray for others?

One doesn't need a fog of purple prose from Torrey or anyone else. What possible purpose is served? If none, why would the apostles suggest it?

But what does that position leave for petitionary prayer? Isn't it true that the determinist model leaves no real expectation of an answer to petitionary prayer for others?

No, that is not true, there is expectation that leads to praise when God's will is carried out.

what purpose is served in asking for anything (particularly for others) in sincere prayer to God? What possible purpose is served?

It gives God the glory due to Him.

If none, why would the apostles suggest it?

It is more than a suggestion, it is commanded.

What if you were petitioning for "Mr. M" and I was petitioning just the opposite for "Mr. M" in my prayers, in your model does God flip a coin?