If Cuba were to enter into a trade agreement with an Asian country in 1903 without US approval, it would have had significant consequences on the relationship between Cuba and the United States.

At the turn of the 20th century, the United States had a vested interest in the political and economic affairs of Cuba. In 1898, the US intervened in the Cuban War of Independence against Spain and subsequently became an occupying power in the country until 1902. As per the Platt Amendment, the US government retained the right to intervene in Cuba`s affairs and control its foreign policy.

In this context, if Cuba had entered into a trade agreement with an Asian country in 1903 without the approval of the United States, it would have been seen as a direct challenge to US hegemony in the region. The US government would have likely viewed it as a breach of the Platt Amendment and a threat to its strategic interests.

Moreover, such a trade agreement would have had economic repercussions for both Cuba and the United States. The US was an important trading partner for Cuba, and any attempt to undermine that relationship would have had significant consequences for the Cuban economy. At the same time, the US would have likely retaliated by imposing trade barriers on Cuban goods, further damaging the Cuban economy.

In the long term, such a move by Cuba would have had far-reaching implications on the country`s relationship with the US. It would have strained the already fragile relationship between the two countries and could have resulted in further interference by the US in Cuba`s affairs.

In conclusion, if Cuba had entered into a trade agreement with an Asian country in 1903 without US approval, it would have been a significant challenge to US hegemony in the region. It would have had economic repercussions for both countries and strained their relationship further. Ultimately, it would have been an ill-advised move for Cuba that could have had long-term consequences on its affairs.