I'll start by saying English isn't my first language, so please, if I make too many mistakes, feel free to point them out and I'll do my best to correct them.

The military school was founded in 1751, using the molds of Russian and Prussian military academies, the curriculum was based on scientific disciplines serviceable to a future officer, those disciplines were:

• Mathematics: This was taught with the idea of familiarizing all officers with problem solving techniques, making them able to serve in all branches of the army, but especially on the engineer and artillery branch.
• Physics: Same idea as math.
• Mechanics and Hydraulics: Aimed at the future engineers and artillery officers.
• Geography: It was aimed at topography, teaching officers to recognize more advantageous terrain.
• Drawings: Mainly military drawings, so they would be able to make plans in any situation.
• Fortifications: This is important, because when artillery started being used, the old medieval fortress weren't effective against them, so a new type of fortification surged specifically made to resist artillery.
• History
• Military Theory
• Languages (French, German, Italian, Latin)

This curriculum was made for nobles and aristocrats, preparing them for serving in the army, while also preparing them for the political life, in some other schools, dance was taught for example; they also mention the necessity for one to learn even after they left the institution, that means the curriculum also tried to lay those foundations for learning on their own.

I couldn't find explicit examples of military exercises, but the subject of artillery theory and artillery drill & exercises are mentioned, as well some more "normal" exercises (think of horsemanship for example). There is mention of music being used to teach more precise and effective battalion moving and coordination, "The idea of dancing into battle placed music at the center of projects to order not just individual bodies, but whole battalions. The musical technology at work in dance could be applied to ever greater numbers" (Van Orden, Music, Discipline, 189.)

I have to state the curriculum was ever changing throughout the years, some disciplines were added while others were removed, it's difficult to keep track of all the dates, so I left pretty much the disciplines who weren't touched for a long time, or at least received minor alterations in comparison to others, but remember that it focus was creating a disciplined, subordinated individual.

I'll recommend the book "The École Royale Militaire: Noble Education, Institutional Innovation and Royal Charity, 1750-1788" by Haroldo A. Guízar for a much in-depth information and sources on this subject.

I must apologize because I couldn't find anything useful for British, Austrian, Prussian and Russian artillery, but I have found this article who tackles the evolving tactics used in artillery battles, it mentions Prussian tactics and also Austrians one, "The Roots of Artillery Doctrine: Napoleonic Artillery Tactics Reconsidered" by Bruce McConachy.

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Sources:

• Julia, Dominique, and Marie-Madeleine Compère. "École militaire." Publications de l'Institut national de recherche pédagogique 10, no. 3 (2002): 413-422.
• Guízar, Haroldo A. The École Royale Militaire: Noble Education, Institutional Innovation, and Royal Charity, 1750-1788. Springer Nature, 2020.