when a semicolon is used is it capitalized
Sentence (a) is correctly punctuated. You should not capitalize after semicolons since the semicolons are simply separating units in a series that contains commas. Nor should you use periods, since the phrases are not complete sentences. The article the is unnecessary before invaluable.
You can also use a semicolon when you join two independent clauses together with one of the following conjunctive adverbs (adverbs that join independent clauses): however, moreover, therefore, consequently, otherwise, nevertheless, thus, etc.