a spark of hope
Act rather than give up hope!
Cross my heart and hope to die!
glimmer of hope
Hope dies last
I [should] certainly hope so.
I hope he reciprocates/returns my affection/love
I hope I was of help to you
I hope she gets her just deserts
I hope that my plea will not fall on deaf ears
I hope this will not happen again in future
I hope to find you in good health
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