Learn Hardcore Portuguese (Portugal): Eu quero definir um plano simples para o exame. - I want to define a simple plan for the exam.

Both are correct and mean the same. In Portuguese the verb form quero already shows the subject (eu), so the pronoun is optional.
People often drop eu in speech unless they want to emphasize I (as opposed to someone else).

What is the verb form quero exactly, and how is it conjugated?

Quero is the 1st person singular (I) of the present indicative of querer (to want):

eu quero – I want
tu queres – you want (informal singular)
ele / ela / você quer – he / she / you (formal) want
nós queremos – we want
vocês / eles / elas querem – you (plural) / they want

So eu quero literally means I want.

Why is it quero definir and not something like quero defino?

In Portuguese, when querer is followed by another verb, that second verb normally stays in the infinitive:

quero definir – I want to define
quero estudar – I want to study
quero descansar – I want to rest

You never conjugate both verbs in this structure, so forms like quero defino are incorrect.
Think of it as directly matching English want + to + verb.

Is quero too direct? When would I use something more polite?

Quero is neutral and common in everyday speech, but it can sound quite direct in requests, especially in Portugal.

More polite or softer alternatives:

Eu gostava de definir um plano simples para o exame.
(Literally: I would like to define…, very commonly used, sounds gentle.)
Eu queria definir um plano simples para o exame.
(Imperfect form, often used as a softer I wanted to… / I would like to….)

For stating your own intention (not a request), eu quero is perfectly normal:

Eu quero definir um plano simples para o exame.
= I want to set up a simple plan for the exam (just stating your goal).

What is the nuance of definir here? Could I just say fazer um plano?

Definir means to define, to set, to establish and sounds a bit more deliberate or structured:

definir um plano – to define / set out a plan (often a bit more formal or careful)
fazer um plano – to make a plan (more general, very common)
estabelecer um plano – to establish a plan (quite formal)

In normal speech in Portugal, fazer um plano is very common; definir um plano can sound slightly more formal or precise, like deciding on the exact details.

Why is it um plano simples and not um simples plano? Is there a difference?

Yes, the position of simples can change the nuance:

um plano simples
= a simple plan (not complicated; straightforward)
um simples plano
= just a plan / merely a plan (emphasizes that it’s nothing more than a plan; only a plan)

In your sentence, um plano simples is the natural way to say that the plan itself is uncomplicated.

Is simples agreeing with plano? Why doesn’t it change form?

Simples is an invariable adjective in terms of gender and has the same form in singular and plural:

masculine singular: um plano simples
feminine singular: uma ideia simples
masculine plural: planos simples
feminine plural: ideias simples

So only the article and noun change (um / uma / planos / ideias), but simples stays the same.

Why is it para o exame and not just para exame?

Portuguese normally uses a definite article with many nouns where English might also have the:

para o exame – for the exam
para a aula – for the class
para o trabalho – for work / for the assignment

Saying para exame (without the article) is grammatically possible but would sound odd or incomplete in this context. You almost always specify o exame, sometimes with more detail:

para o exame de matemática – for the maths exam

What does para express here? Could I use another preposition like a or de?

Here para expresses purpose / goal:

um plano simples para o exame
= a simple plan for the exam (with the exam as its purpose/target)

Other prepositions would change the meaning:

plano do exame – the plan of the exam (as if the exam itself has a plan)
plano ao exame – incorrect in this sense

So for a purpose (for the exam), para is the natural choice.

What is happening in para o? Is that a contraction?

Yes, in writing you see para o, but in speech it’s usually pronounced as a contraction:

para + o exame → spoken very close to paro exame

In standard spelling, para o normally remains two words, unlike other prepositions that must contract:

de + o exame → do exame
a + o exame → ao exame

So:

written: para o exame
spoken: sounds like one unit, roughly paro exame in European Portuguese.

How is exame pronounced in European Portuguese?

In European Portuguese:

exame ≈ [e-ˈzɐ-mɨ]
- e: like the e in get (but a bit more closed)
- xa: pronounced za, like za in pizza
- me: the final e is not silent; it’s a reduced sound ɨ, similar to an unstressed uh.

So it’s closer to eh-ZUH-m(ɨ), not like the English exam and not eg-zame.

Can quero here express a future intention, like “I’m going to define a plan”?

Yes. In Portuguese, the present of querer plus an infinitive often implies a future intention:

Eu quero definir um plano simples para o exame.
= I want to define / I’m intending to define a simple plan for the exam.

For a more direct future plan, you could also say:

Vou definir um plano simples para o exame. – I’m going to define a simple plan for the exam.

Quererei definir… (future of querer) exists but is rare in everyday speech.

If I replace um plano simples with a pronoun, where does it go?

If you refer back to o plano with a direct object pronoun (o, meaning it), in European Portuguese you usually attach it to the infinitive:

Eu quero defini-lo para o exame.
= I want to define it for the exam.

Structure:

definir
- o → defini-lo

In this kind of sentence in European Portuguese, forms like Eu o quero definir are not natural; the normal option is to attach the pronoun to definir (the infinitive).