My dean once told me, "Remember where you're sitting." Approach this with respect for the professor and from a position of strength, not with disdain for the professor and from a position of weakness. Your best chance is to ask for probation, but you must also admit a no-brainer. It's all in here, try this:
I am writing concerning the two absences I was deducted on account of reading unrelated textbooks during class. I request probation to have the statutory absences removed, but only on the condition that during finals I present responsible class notes for the remainder of the semester. As an engineering student, I should know that reading a textbook applies to the same principle as a the policy ban on mobile screens in class. Though this is an introductory class, covering information with which I consider myself to be familiar, I will hold a newfound respect for the importance of both foundational skills and the value of reviewing them. My grades are of concern to me, so if you as the lecturing professor will not grant me an achievable probation, I would only exercise my right to appeal by forwarding this same letter to the department chair, but I would go no further.
IME, this is your best chance. You can take suggestions from anyone, but it's still your own decision which course of action to take; whatever the results, the blame or the credit all goes to you.
Brief explanation: The goal is not to prove a prof wrong at the price of -5%; the goal is to reverse two special absences, and keeping peace is the best chance here. Every step of this letter does that.
To respect the community, I'm adding notes to explain, feel free to skip:
In my background, this isn't just theory, I wrote a letter to my school and had the student rules changed mid-semester. I also wrote a letter to Chicago and had the no-parking curbs painted yellow the following month. I've done more elsewhere and I know how to draft a letter that wins. The secret is that everyone needs to win and folly needs to be set in a third seat no one is forced to sit in.
No matter the outcome, no one loses face with this. If the prof permits the "probation", then the prof doesn't have to admit any wrongdoing. Never ask your opponent to admit guilt as a requirement of granting your request.
The word "statutory" is vital because in a busy administration, these must be regarded as a kind of "technical foul", not actual, normal absences. The student has three actual absences, so there is a good chance for confusion. Any other word would require more words or be confusing. This makes everything clear.
Offering to keep good notes reflects the "original intent" of the prof's policy and a "coming into the fold" to support what "good attendance" is all about. It is also a way of "eating crow", a necessity to get probation anywhere, and the student gladly wears the dunce cap, but with a straight back, self-dignity, and gratitude to the prof for a punishment well-deserved. It shows dignity across the board, including the self-dignity of growing up and becoming a better person, which is what college is all about.
Engineering students should know the cross-media application. In the 1990s and before it was reading magazines. Today, it's playing on handhelds. Engineers produce "products" that fulfill the same, age-old purposes in society, but using technology for the time and purpose. An engineer who doesn't see the carry-over will have difficulty working with a product manager in the field. Moreover, that might have been covered in one of these boring, elementary (but vital) lectures.
Foundation, foundation, foundation—that is essential to any discipline. Also, this student might need to explain these principles to a product manager or a design team one day. Listening to this prof put things in simple terms might not only be for the students to learn, but also serve an example for what the students can say to teach other departments in a future company. Showing gratitude for this teaching method's "value" is wise.
"My grades are of concern" is the toned-down way of saying "It's my prerogative", which would be too wordy. Any student should be concerned about grades; some aren't! This student is one of the good students. And, it is perfectly understandable and reasonable that a student take steps to attain better grades, even with some normal college-age immaturity elsewhere. Any decent student would be foolish not to appeal for better grades if there were grounds for an appeal. Say so!
The final sentence might wrongly seem like a threat to some people. However, this is no more than a respectful reminder of the student's own rights. Always state your rights and that you may exercise them in any administration, whether school, government, courts, or any other. If anyone might feel put off by this, that could indicate a need to either learn about respecting the rights of others or to examine one's own motives. Why would you having rights make someone else feel threatened? What kind of a person would feel threatened by someone else having rights? With such a person, there is no way to win, and there would be nothing good or kind enough to say. But, I don't think that's the case here. This prof seems like a good person who genuinely wants students to learn because, though arguably harsh, the rules aren't totally unreasonable. Such a good person as this professor should not be offended merely by someone else reminding everyone of known rights.
Stating specifically how the student would make an appeal means that the student won't try to walk on the prof, but won't be walked on either. The prof knows what would happen, no surprises. So, the prof could go to the chair first and ask first, making a decision that won't be overturned by any appeal either way. Again, this allows saving face. If the student appealed, the chair is already in a position to respond, "I already know about this. The decision is final," yet the student wouldn't be seen a fool since the chair knew because the student said as much, nor would the faculty be seen as "gossipy". Everyone wins here, no matter the decision. Most importantly, saying "but I would go no further" means that the student will accept the decision and not keep beating a dead horse, something many people do. Say right away that you're not like that.
How to deliver & respond:
Print on computer, no headers, only "Dear [PROF]" and a normal first-last name closing, sign with "Your student, [NAME]". You could make the entire request in handwriting, but DO NOT SIGN with the John Hancock! DO NOT EMAIL! Go in person, at least to deliver. Emails can be scary, especially anyone watching the news lately. Emails are convenient in daily life, but in conflict they are limited and lazy—can't solve conflict. Take time to deliver a note in person, be soft, friendly, informal, "via memo"—all these things add a pinch of kindness and a dash of diplomacy—things this situation needs all it can get of. Everyone can save face by this being informal. But, having it on paper, the prof can go directly to the chair and ask for advice, having the options of doing so formally or informally; we want that. Administrations should have the power to administer, and in administration do everything in writing. Respect administration and administration will respect you.
The student could drop it in the prof's mailbox or pin it to a board outside the office, whatever works. If delivered in person, be charming and humble and thankful. Even if the prof denies the request, be thankful for the learning opportunity, sit in the front row, and take double notes the rest of the semester. The best argument is "hard work" and could result in the grades not being lowered, even if the prof says no at first. Kindness and respect melts hearts.
Remember, profs are humans who deserve attention, even in survey lecture halls. They genuinely want students to learn. Their strange rules often come as a way of trying their best to help students learn what they will need.
Administrations are made of rules and respect hierarchies by definition; bucking against either will only cause brain damage.
Being a sesquipedalian is actually a good idea because academic journals are the sacred texts of academia; when in Rome... The key is to not use big words that confuse meaning because they aren't needed. Though it could be toned-down, that's not the case here.
Lastly, even in admitting wrong—the student should don the dunce cap here, but do so thankfully and respectably—NEVER, NEVER, NEVER do this: "I'm right because... but I'm sorry and you're right." Don't be a wet noodle; stand up and act like you have a spine, say "I need to act respectable by respecting the prof!" What good prof could resist the urge to honor that! But, that self-justify-then-roll-over approach is Satir's Blamer-Placater Distracter Mode and is half a penny shy of a formal request for a public beating.
In school, the purpose is to learn. So, prove that you're good in school by proving that you are learning. Learning is your best defense and work demonstrated is its best evidence.