You have done well by forming this good intention for your exercise, for a good intention turns a habit into worship.
As for what you have asked about, whether praying for forgiveness increases a person’s strength, the answer is, yes. Allah, may He be exalted, tells us that His Prophet Hood (peace be upon him) said to his people (interpretation of the meaning):
“And O my people! Ask forgiveness of your Lord and then repent to Him, He will send you (from the sky) abundant rain, and add strength to your strength, so do not turn away as Mujrimoon (criminals, disbelievers in the Oneness of Allah).”
Ibn al-Qayyim said in al-Wabil al-Sayyib (p. 77), when listing the benefits of dhikr (remembrance of Allah), including praying for forgiveness:
Benefit no. 61:
Dhikr gives a person strength so that he can do with dhikr that which he cannot do without it. I saw wonders in the strength of Shaykh al-Islam Ibn Taymiyah in walking, speech, courage and writing. He used to write in one day what a scribe would write in a week, or more. The troops saw his amazing strength in war. The Prophet (peace and blessings of Allah be upon him) taught his daughter Fatimah and ‘Ali (may Allah be pleased with them) to recite tasbeeh (glorification of Allah) thirty-three times every night when they went to bed, and to recite tahmeed (praises of Allah) thirty-three times, and to recite takbeer (magnification of Allah) thirty-four times, when she asked him for a servant and complained to him about the hardship of grinding corn, working and serving (her family). He taught her this and said: “It is better for you than a servant.” It was said: The one who persists in doing this will find strength in his body that will make him independent of the need for a servant. End quote.
With regard to the times for dhikr and the number of times it should be repeated, the believer should remember Allah at all times and in all situations. Allah says (interpretation of the meaning):
“Those who remember Allah (always, and in prayers) standing, sitting, and lying down on their sides.”
[Al ‘Imran 3:191]
The Prophet (peace and blessings of Allah be upon him) would remember Allah at all times. Narrated by Muslim.
So one should remember Allah a great deal and pray for forgiveness. The more he does that, the better.
Allah says (interpretation of the meaning):
“O you who believe! Remember Allah with much remembrance.
And glorify His Praises morning and afternoon [the early morning (Fajr) and ‘Asr prayers].”
[al-Ahzab 33:41, 42]
“... and the men and the women who remember Allah much with their hearts and tongues. Allah has prepared for them forgiveness and a great reward (i.e. Paradise).”
Muslim (2702) narrated from al-Agharr al-Muzani (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) said: “I ask Allah for forgiveness one hundred times a day.”
And Abu Dawood (1516) narrated that Ibn ‘Umar (may Allah be pleased with him) said: We used to count when the Messenger of Allah (peace and blessings of Allah be upon him) said in one sitting one hundred times: Rabb ighfir li wa tubb ‘alayya, innaka anta al-tawab al-raheem (Lord, forgive me and accept my repentance, for You are the Accepter of repentance, the Most Merciful). Classed as saheeh by al-Albani in Saheeh Abi Dawood.
And Allah knows best.