MacBook Air Battery is not charging, no light, still be able to power up, battery condition is normal

There's a number of confounding things going on here: Firstly, there's the fact that rendering an output changes the time something takes to compute:

A fairer way of timing the two would be:

RepeatedTiming[Integrate[x^2 + x, {x, 0, 1}];, 2]
RepeatedTiming[Integrate[x^2, {x, 0, 1}] + Integrate[x, {x, 0, 1}];,
  2]

{0.0015, Null}

{0.0019, Null}

With a slightly longer time to compute the separated integrals, as one might expect as there is an additional calculation.

Then there's the way in which arguments is presented,

arguments1[[1]]

1+x+O[x]^2

Which is given (and integrated) as:

SeriesData[x, 0, {1, 1}, 0, 2, 1];

Fixing this by adding //Normal to the line, significantly impacts the results:

arguments1 = Table[Series[Exp[x], {x, 0, i}], {i, 1, 200}]//Normal;
arguments2 = Table[MonomialList@Normal@Series[Exp[x], {x, 0, i}], {i, 1, 200}];//Normal

Without //Normal:

With //Normal on arguments1:

With //Normal on both arguments1 and arguments2:

l1 = LinearModelFit[timings1, x, x] // Normal;
l2 = LinearModelFit[timings2, x, x] // Normal;
Show[ListPlot[{timings1, timings2}, PlotRange -> All], 
 Plot[{l1, l2}, {x, 0, 200}, 
  PlotStyle -> {{Thick, Purple}, {Thick, Red}}]]

As you can see, in this situation both grow about approximately linearly, and the integral calculated together is nominally faster as expected.

This also more or less fixes the Memory issue, though as always with such things there are anomalies

Let us assume ZFC is our set theory.

Given a model of set theory, $M$, we always have that $M$ thinks $\mathbb R^M$ (what $M$ thinks is the real numbers) is of cardinality $2^{\aleph_0}$. It is a theorem of ZF that $\mathbb R\sim{\cal P}(\mathbb N)$, so from the internal point of view $M\models|\mathbb R| = 2^{\aleph_0}$. This, however, does not say much about what $\alpha$ we have $|\mathbb R|=\aleph_\alpha$.

Using forcing we can always ensure there is some $M\subseteq M'$ such that $M'\models|\mathbb R|=\aleph_1$, we may have added real numbers in the process, but we can ensure that in $M'$ this is the situation.

Now given $\kappa$ which is uncountable we only have one requirement from $\kappa$ that $\operatorname{cf}(\kappa)>\aleph_0$, we can now add $\kappa$ many real numbers via forcing to have $M\subseteq M'\subseteq M''$ such that $M''\models |\mathbb R|=\kappa$.

This covers all the cardinals except those with countable cofinality. Suppose now that we started with $M$ such that $M\models CH$, we may collapse $\aleph_1$ to be countable, namely find $M\subseteq M'$ such that $M'\models|\omega_1^M|=\aleph_0$. In the new model we have added real numbers, however externally we have that $M$ is a model in which there are only countably many real numbers.

I cannot give you a concrete answer about singular cardinals of countable cofinality, however I can make a remark about a symmetric extension (i.e. a submodel of a forcing extension):

Start with a model of CH, $M$, and collapse all the $\aleph_n$'s to be countable. We effectively added $\aleph_{\omega+1}$ many real numbers. So we have $M'$ such that $\aleph_{\omega+1}^M=\aleph_1^{M'}$.

Now there is a submodel, $M\subseteq N\subseteq M'$, in which the axiom of choice does not hold, where the continuum is a countable union of countable sets(!!). From $M'$ view (an external point of view) $N$ has $\aleph_\omega$ many real numbers. I believe that this argument can be done with every singular cardinal of countable cofinality, however I did not check that.

Your requirement can be achieved by Process Builder

These are the steps:

Choose Object

Account (Start the process = When a record is created or edited)

Define Criteria

Account.Quote_Methods__c is changed

Update Records

Records [Account.Opportunities]

Field: Quote_Instruc reference [Account].Quote_Methods__c

If any changes made on Quote_Methods__c of Account record, it will update Quote_Instruc__c of all the opportunities.

By the way, in case you want to update any specific opportunities then Trigger is the only option.