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modernの意味 - goo辞書 英和和英
近代的(or 現代的) is used as the antonym of ancient, classical, medieval, (古典的, 中世的), so 近代的なコンピューター is used in the context that it refers to "computers" we are using now as the contrast to archaic/classical "computers" such like
soroban or slide rule. On the other hand, 最新式のコンピューター means "the newest / new model", as in the kanji.