Faith, like you said is about "trusting" what one believe in. Nothing in "faith: (definition) say any about believing anything about "evidence" or "logic". You are attempting to twist what faith mean, by adding terms that associate with "faith".
Yes, faith is trusting. You can trust in something blindly, or you can trust in something after you have evidence, or if you have reasons to trust. I trust my mother to hold onto my personal items. Why? Because I've known her my whole life, she has taken care of me and never did anything that would put me to harm. So if I had an important object that I needed to keep safe, I would be able to put my faith on my mother to keep it safe with her and not give it away or steal it. That is called faith with reason. Blind faith is where you see a random person on the street and blindly trust them for your things. The thing is, you can never be sure what type of person they are and what they will do with your things.
Faith is a neutral word, and is applied depending on context.
When we talk about faith in God, it's the same deal. A person will either have faith in God without any reasons, or with reasons. There's nothing wrong with both, but the person who has faith in God with reason will be the stronger believer, because they had experienced what the blind faith one did not, and that is a fulfillment of trust.
Take for instance, Muhammad's claim that he is prophet because of an angel named Gabriel said so. How do you know? There were no other eye-witnesses to collaborate his angelic encounter, except for Muhammad's words alone. That's faith, that you believe it is true, not evidence.
People believed in Muhammad not because he just told them, "Oh look at me, an angel spoke to me and I'm a prophet." People believed in Muhammad because they knew him his whole life, and that he was a sane person whom was also honest and trustworthy, never would he tell a lie. Just like I trust my mother to hold onto my things. Muhammad's friend, Abu Bakr, was on an expedition when Muhammad claimed prophethood, and upon his arrival back home, he heard that Muhammad claimed prophethood. He went up to his house and Muhammad began to speak and start giving his friend reasons and evidence for his claim of prophethood, and Abu Bakr told him to stop, and that he believed in him without needing any evidence.
Why? Because his friend knew him his whole life, that Muhammad would never lie, nor was he insane or had mental instability. And that is how the first believers were those of Muhammad's close family and friends, and nobody else, for the first three years. Muhammad's close ones knew him and his personality, so they trusted him, just like I trust my mother whom I knew my whole life.
If Muhammad was a random stranger who appeared in Mecca and told everyone to follow him since he's a prophet, that would be a different story. In the other case, his family and friends had good reason to believe him. In this new case, if Muhammad was a random stranger, there are no good reasons to follow or accept him, since anyone can easily claim prophethood, and many did after Muhammad's death.
When we talk about God, God guides those people who search for Him and investigate Him. The Qur'an already talks about revealing signs and miracles (in Arabic, ayat), which are evidences for His existence. God reveals His ayat to those who already have open hearts, those who are searching for truth. He doesn't guide those who think they know everything, and many atheists act this way, as if they know for sure there isn't a creator. The arrogant will never be guided.
I don't respect your dishonesty for trying to twist the meaning of faith with the context of evidence or logic. You implied that faith mean evidence and logic, but that's not true.
And where exactly did I say that? I don't respect your strawman argument.
