correct: He was so upset that he had to cool his aggressions.
incorrect: He was so upset that he should cool his aggressions.

correct: She was so enraged that she had to cry.
incorrect: She was so enraged that she should cry.

correct: The car was broken down so we had to leave it behind.
incorrect: The car was broken down so we should leave it behind.

correct: He didn't find another possibility. He had to do it.
incorrect: He didn't find another possibility. He had to do it.

Si quieres pasar el examen, tienes que estudiar más.
= If you want to pass the exam, you have to study more
Se quebró una pierna asi que tuvo que quedarse en casa.
= He broke a leg, therefore he had to stay home.
Hizo tanto frío que incluso los osos tuvieron que quedarse en su cueva.
= It was so cold that even the bears had to stay in their cave.
Cuando se le acabó el dinero tuvo que abandonar el proyecto.
= When the money was used up, he had to stop the project.
Si quieres ser más delgado tienes que comer menos.
= If you want to be slimmer, you have to eat less.
Estuvo tan cansado que tuvo que echarse a la cama.
= He was so tired that he had to lay down in bed.