## Function providing input and integration limits for NIntegrate

I am trying to define some custom function that evaluates the numeric integral of some complicated function. The problem is that I would like to include as an input the integration limits. A MWE follows

f[x_,y_]:= Exp[-2 x^2 y^2] test[x_?NumericQ,IntL_]:= NIntegrate[f[x, y],IntL] myIntL1= {y,-4 x^2,4x^2}; myIntL2= {y,-4 x^4,4x^4};

Then, if I evaluate for instance test[3,myIntL1] I get a problem concerning an invalid limit of integration.

Is there a clever way to fix this without defining several functions including the integration limits, such as

test1[x_?NumericQ,IntL_]:= NIntegrate[f[x, y],{y,-4 x^2,4x^2}]     test2[x_?NumericQ,IntL_]:= NIntegrate[f[x, y],{y,-4 x^4,4x^4}]

etc?

Of course, here everything looks simple, but in my case all the functions are rather long; some even purely numeric ones. Since I have multiple choices for the integration limits, it would be more practical to avoid defining test1[x_], test2[x_], ..., testN[x_]

Thanks in advance, Pablo

## Limits of an Aboleths Enslave

The rules for an Aboleths Enslaved relate largely to combat situations but what are the limits of what A charmed person would do for an Aboleth.

For instance could an Aboleth convince an enslaved person to sacrifice themselves to raise a demon, or to die in order to hide a secret (for instance if captured or caught)?

## D&D 5e:Spell Scroll Limits With Multiclassing

I have a druid with the ability to cast level 5 spells. If I multi-class this druid to be a level 1 cleric, In theory, I should be able to read and use any cleric scrolls.

But in the PHB, it says

If the spell is on your class’s spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully. The DC equals 10 + spell’s level. On a failed check, the spell disappears from the scroll with no other effect.

Now here is the conundrum, If I were to use a level 5 cleric scroll (like Hallow) Since I can normally cast level 5 spells, (even some cleric spells because of my druid circle) Would I have to make this check because I am a level 1 cleric, or do the rules mean what they literally say here, that as long as the spell is not above a level which I can normally cast, I do not have to make the check. Is there a further clarifying rule about this I am missing or is this just something inherently vague that the DM would have to decide?

## What are the limits of Mage’s Magnificent Mansions?

I am DMing true D&D for the first time. So far it has been one of the most fun experiences in my life. However, I have found myself in a bit of a pickle. Starting off I was very liberal in what I allowed my players to create and do, and now am seeing the problems of this break out in my world. So, now I am tightening the leash a little bit. One player in particular has a very powerful Rakshasa sorcerer and recently has started using the Mage’s Magnificent Mansion spell to create a restaurant and sell the food from inside. He is trying to weave a network of mansions from different points together to create a instantaneous fast travel system. The player states that the rules are genuine, but I’m not so sure it I agree. Are there any limits to the this spell in the rules? Can he have more than one mansion at one time and can his servants leave the mansion to act as staff in an eatery?

## What are the drawbacks of placing time limits on turns?

I personally find general concept of enforcing time limits on player turns during combat a very, very good thing for the following reasons:

• Just like in a real battle, you don’t have a lot of time to think. Time limit represents this quite well.
• You don’t have enough time to get distracted until you are acting again, no time is wasted while you think of something else, check Facebook feed etc, because waiting for everyone to finish may get boring.
• You can go through more encounters per hour, combat doesn’t take forever to resolve.
• Combat becomes much, much more intense.

Etc, etc.

How I suppose time limits to work:

• You are only allowed to talk during your turn. That includes no asking for any clarifications, tactical advice, discussing what goes on while it’s not your turn.
• While turn of the player who acts before you starts, GM calls out your name and says that your turn is next.
• When that player has acted and math is applied, GM describes what has changed. You are supposed to listen carefully, GM doesn’t describe what’s happening for each player individually. Sometimes it can take 10 seconds, sometimes minutes — doesn’t matter.
• Your turn starts, you have 30 seconds per action your character can do. During that time you are supposed to tell the GM what are you doing and roll dice. Math doesn’t count. If you need any clarifications, you have to use those 30 seconds. Same if you want to say something to anyone in-character during combat. Once you roll, you stop talking, GM counts and announces the result of your roll and current situation.
• If you don’t both describe your actions and roll dice during those 30 seconds, which most likely means that you didn’t have any plan in your head, you make a “default action”, which is decided in advance.
• If you only described what you want to do partially and your time ran out, you have ~3 seconds to say if you do what you had time for to describe, if you perform a default action of if you do nothing.
• Of course, people may ask for a game to pause if they need to bring some tea, answer phone etc. After all, such intense combat may get people tired.
• GM describing what goes on between your actions doesn’t count.
• Taking a full-round action has to be described during your first 30 seconds. If you don’t do it, you cannot perform a full-round action that round, and one of your actions is lost as usual. Though, you might (in advance) name any full-round action as your default action.

The only real problem I see is that new players need more time to think anyway, sometimes even some help from others, but there are some experienced players who object to such solution.

I am myself new to Pathfinder E6, which I am going to use this solution for, so answers related to this system are most welcome.

What are the drawbacks of setting time limits on turns?

I expect answers stating exact problems that were caused by time limits actually observed during gameplay.

## What are the limits of the Conception spell?

Conception is an interesting spell.

With the casting of this spell, you guarantee that on your next attempt, you and your partner will conceive a child. Conception overcomes sterility or infertility in either you or your partner, whether natural or due to an injury, illness, or curse, as well as herbal remedies that normally block conception. Alchemical or magical means of blocking conception, such as block the seed, counter conception and make the spell ineffective. (…)

This spell came up during an intrigue-related game. One of the players wants to guarantee that the queen will get pregnant from her lover to further their schemes. They planned to trick the lover into drinking a Potion of Conception, in the hopes of jumping over the barriers related to the queen’s supposed infertility.

That’s all good and fine.

Except the queen and her lover aren’t exactly from compatible species.

They don’t know yet, but the queen is actually a synthetic construct – a warforged-like being made to look exactly like a human being at any external inspection, with most of the functioning bits and pieces (she can eat, go to the toilet, cry, have carnal relationships, salivate, etc) while being effectively immortal, able to replace any part that is breaking down due to old age or damage by a quick visit to her automated repair chamber.

Obviously, if it was the queen the one to drink the potion, I would just rule that her anatomy is too alien and the potion has no effect. However, it is her lover that is drinking the potion. By a RAW reading of the rules, this synthetic, infertile replicant will end up getting somehow pregnant after the next session with her lover, even if no viable offspring was possible between then.

I can’t even rule that she "doesn’t have the proper equipment", because the spell overcomes sterility/infertility, be it natural or caused by some source. Since the queen is a synthetic being that is "naturally" infertile, the spell appears to work at a first glance, but I might be missing a nuance somewhere.

So:

• If my players proceed with the plan, will the Replicant Queen get pregnant?
• If she does, what would be the race of the child?
• Would the queen still get pregnant if she was actually a Lich in disguise?

About the "Attempt" angle: If "willingness to conceive" from the part of the spell recipient is necessary, consider it present.

## Limits to appearance of a phantom steed

In a recent game session, a player wanted to become invisible and then use a phantom steed to quickly and stealthfully pass through the enemy camps surrounding a besieged city. This began a discussion of whether the phantom steed summoned could be transparent, or nearly so. The spell says:

A Large quasi-real, horselike creature appears on the ground in an unoccupied space of your choice within range. You decide the creatureâ€™s appearance…The creature uses the statistics for a riding horse

So what are the limits to the appearance of the steed? While "quasi-real", can it be made to appear so real that an observer would believe it to be a real horse? Can it be made to appear so unreal as to be seen through and receive a bonus on Stealth?

For the limit on how transparent it can be I thought the important restriction is that it has the stat block of a riding horse. Any permanent bonus to Stealth would be included within this block, and a riding horse does not have one. Thus, for me the mechanical limit to transparency would be that it could get a DM-assigned circumstantial bonus (advantage to Stealth checks depending on situation) but not a permanent bonus irrespective of circumstances (modification of stat block).

For the limit on how real it can appear, I looked to the spell Major Image, as an Illusion spell of equal level, whose illusions have the following property

A creature that uses its action to examine the image can determine that it is an illusion with a successful Intelligence (Investigation) check against your spell save DC.

Thus if the steed was summoned to appear real, it would fool any observer who was not explicitly trying to determine its nature, and even some of those depending on the roll. This approach of comparing the spell to same-school spells of equal level comes to me from 1e, with which I have more experience, and in which spells are much less clearly defined in terms of their limits. 5e, on the other hand, has the general principle that "spells do what they say they do". Is such a comparison to another spell then valid?

1. What are the limits to the appearance of a phantom steed? How real or unreal can it appear?

2. When deciding (1), is it useful to compare the spell to Major Image?

## Mathematical limits on lossless data compression

Let’s say Bob wants to send a particular binary sequence to Alice. Imagine that Bob and Alice both have powerful machines but slow Internet connections. Bob could just send the sequence directly but the upload and the download would take a lot of time. Instead Bob could send a program that outputs the sequence. Assume Bob and Alice have agreed on the programming language they will use beforehand (be it C++ or Iota).

Two natural questions are what is the smallest possible size of the source file and how to find a program attaining the lower bound for a given sequence (e.g. can it be done algorithmically for any sequence or at least for some sequences). Have these questions been studied?

## What are the limits of the Purrodaemon’s Weapon Steep ability?

The Daemon, Purrodaemon ability "Weapon Steep" states:

If a weapon remains sheathed in its body for at least 24 hours, the weapon absorbs some of its essence and gains magical enhancements. A purrodaemon can have up to a dozen weapons lodged in its body at a time, but only one can possess magical enhancements at a time. The total enhancements cannot exceed a +4 effective enhancement

Can this ability be used enhance an already magic weapon further? For example: Purrodaemon steeps a +1 Impact Guisarme. Can he then add up to a +4 enhancement to that weapon, such as Brilliant Energy? Or can he only add enhancements to mundane weapons?

## What are the limits to repeating a move in Dungeon World?

As far as I’m informed, you could just repeat a move until you get the desired effect, since there is no cooldown or mana. Are there limits to repeating a move, and if so what are they?