Illogically she had expected some kind of miracle solution.

她本以为会有奇迹般的解决方法，这是不合情理的事。

Illogically, she had expected some kind of miracle solution.

她满以为会有奇迹般的解决办法，这显然不合情理。

Illogically, IT have to HAs expected some kind of miracle solution.

她竟期望会有某种奇迹般的解决办法，这是不合情理的事。

Illogically, she should have expected some kind of miracle solution.

她竟希望会有某种奇迹般的解决办法，这是不合情理的事。（副词分译）