Capitalism is an economic system in which trade, industries, and the means of production are largely or entirely privately owned and operated for profit. Central characteristics of capitalism include private property, capital accumulation, wage labour and, in many models, competitive markets. In a capitalist economy, the parties to a transaction typically determine the prices at which assets, goods, and services are exchanged.
Since all economic systems are descriptions created by scholars & advocates, there is no "real" definition of capitalism beyond what various people think. I tend to agree with the above posters, and Wikipedia, that "capitalism" as it is used in most economic and political discussions today does entail the ability to collect, store, and earn income from market transactions, and that this is conceptually distinct from markets. what I don't agree with is that empirically these things can ever be separated, apart from very limited and highly constrained circumstances. any relatively free market allows participants to hoard, causing supply/demand imbalances; that hoarding eventually turns into capital, if by no other power than by the hoarder's ability to loan out his supply and receive interest income (aka "rent") from the party lent to. i am completely unconvinced by the libertarian socialist arguments for free markets without capitalism, especially given the libertarian commitment to (at best) a "night watchman" state: without constraints on hoarding and manipulation, and without some worldwide and unimaginable resetting of the economy so that everyone starts at 0--a resetting that itself would be an amazing political event that would probably obviate any need for this kind of political strategic discussion--those who already have a lot will always be able to use that to their advantage, to corner markets and manipulate supply/demand imbalances. so while "free markets" and "capitalism" are conceptually distinct, my view is that in the real world, you can't have free markets without capitalism. whether you could have capital itself without free markets is a more complex and esoteric question--arguably, to use your example, the USSR functioned as a storer of capital in the world economy, but the international markets were not "free" by anyone's definition.
We have a equal opportunity Calculus class -- it's fully integrated.