My brother felt sick for some reason.
This sentence contains one independent clause. The simple subject is "brother", and the simple predicate is "felt". The prepositional phrase "for that reason" is one part of that one independent clause.
My brother felt sick because of the chocolates.
Even with the word "because", this sentence also contains only one independent clause. The phrase "because of the chocolates" does the same job in this sentence as "for that reason" does in the first example.
My brother felt sick because he ate too many chocolates.
In this sentence, we have two clauses. There is the clause with brother/sick as its subject/verb pairing, and another clause with the pairing he/ate. In spite of that, the entire structure "because he ate too many chocolates" still performs the same function. In all three of these examples, the italicized constituents act as modifiers of the adjective "sick".
Simple substring processing is not a good model for analyzing English. The substring "My brother felt sick" appears in all three example sentences, and yet the clause "my brother felt sick" does not appear in any. The independent clause in each example includes the entire contents of its sentence.
There's a better label than independent clause for the third example. It is a matrix clause -- a clause that contains another clause. The dependent clause is subordinate to its matrix clause.
If you need a computational model, don't look at operators. Look at factories. In the first example, the preposition "for" takes "some reason" as its argument and produces a general modifier, the prepositional phrase "for some reason". That produced constituent (an object, in the OOP sense) is then able to attach to a suitable modificand, such as the preceding adjective.
If we think of "because" as a preposition, as a modifier factory, then we see it has more than one signature. In the second example, its argument is a prepositional phrase. In the third, it's an entire independent clause. We can also see that what it generates not as general-purpose as the constituent produced by "for". It doesn't attach as readily to a nominative construction.
If we're too old-fashioned to think of "because" as a preposition, then we're left with treating "because of" as a compound preposition, taking a grammatical object as its argument. We're also left with labeling the third example's "because" as a subordinating conjunction.
Even under that old-fashioned labeling, this subordinating conjunction is a factory. It produces an adverbial subordinate clause.